首页 > 最新文献

Journal of Mathematical Analysis and Applications最新文献

英文 中文
Full stability characterization of shearing Cattaneo-Timoshenko systems 剪切Cattaneo-Timoshenko体系的全稳定性表征
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2026-01-21 DOI: 10.1016/j.jmaa.2026.130452
Eduardo H. Gomes Tavares , Anderson J.A. Ramos , Marcio A. Jorge Silva , JinYun Yuan
We provide a complete analytical and numerical characterization of the stability behavior for a shearing Cattaneo-Timoshenko system governed by a recently proposed stability number, denoted herein by χτ. Unlike previous results restricted to energy-based approaches or specific parameter configurations, we prove that χτ=0 is not only sufficient but also necessary for exponential stability. Otherwise, the system exhibits optimal algebraic decay rate t1/2 for regular initial data. The theoretical results are aligned with a proper numerical analysis where a finite difference scheme confirms the characterization of stability in terms of χτ and its effectiveness in predicting the complete system's asymptotic behavior.
我们提供了剪切Cattaneo-Timoshenko系统稳定行为的完整解析和数值表征,该系统由最近提出的稳定数控制,这里用χτ表示。与以往的结果局限于基于能量的方法或特定的参数配置不同,我们证明χτ=0不仅是充分的,而且是指数稳定性的必要条件。否则,系统表现出最佳的代数衰减率t−1/2的规则初始数据。理论结果与适当的数值分析相一致,其中有限差分格式证实了用χτ表示的稳定性特征及其在预测完整系统渐近行为方面的有效性。
{"title":"Full stability characterization of shearing Cattaneo-Timoshenko systems","authors":"Eduardo H. Gomes Tavares ,&nbsp;Anderson J.A. Ramos ,&nbsp;Marcio A. Jorge Silva ,&nbsp;JinYun Yuan","doi":"10.1016/j.jmaa.2026.130452","DOIUrl":"10.1016/j.jmaa.2026.130452","url":null,"abstract":"<div><div>We provide a complete analytical and numerical characterization of the stability behavior for a shearing Cattaneo-Timoshenko system governed by a recently proposed stability number, denoted herein by <span><math><msub><mrow><mi>χ</mi></mrow><mrow><mi>τ</mi></mrow></msub></math></span>. Unlike previous results restricted to energy-based approaches or specific parameter configurations, we prove that <span><math><msub><mrow><mi>χ</mi></mrow><mrow><mi>τ</mi></mrow></msub><mo>=</mo><mn>0</mn></math></span> is not only sufficient but also necessary for exponential stability. Otherwise, the system exhibits optimal algebraic decay rate <span><math><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></span> for regular initial data. The theoretical results are aligned with a proper numerical analysis where a finite difference scheme confirms the characterization of stability in terms of <span><math><msub><mrow><mi>χ</mi></mrow><mrow><mi>τ</mi></mrow></msub></math></span> and its effectiveness in predicting the complete system's asymptotic behavior.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 2","pages":"Article 130452"},"PeriodicalIF":1.2,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ground state solutions and asymptotic behavior for a nonlocal Kirchhoff–Choquard equation with variable potential in R3 R3中具有变势的非局部Kirchhoff-Choquard方程的基态解和渐近行为
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2026-01-20 DOI: 10.1016/j.jmaa.2026.130445
Mohammad Saeid Abolhassanifar , Reza Saadati , Mohammad Bagher Ghaemi , Donal O'Regan
<div><div>We investigate a class of nonlinear nonlocal problems that integrate two complex mechanisms: Kirchhoff-type nonlocal diffusion and Choquard-type critical convolution nonlinearity involving the Hardy–Littlewood–Sobolev (HLS) critical exponent. Specifically, we consider the following equation in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>:<span><span><span><math><mo>−</mo><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><msup><mrow><mo>(</mo><munder><mo>∫</mo><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></munder><mo>|</mo><mi>∇</mi><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mspace></mspace><mi>d</mi><mi>x</mi><mo>)</mo></mrow><mrow><mi>θ</mi></mrow></msup><mo>)</mo></mrow><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>u</mi><mo>=</mo><mrow><mo>(</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>⁎</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi></mrow></msup><mo>)</mo></mrow><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>,</mo><mspace></mspace><mi>u</mi><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo><mo>,</mo><mspace></mspace><mi>u</mi><mo>></mo><mn>0</mn><mo>,</mo></math></span></span></span> where <span><math><mi>a</mi><mo>,</mo><mi>b</mi><mo>></mo><mn>0</mn></math></span>, <span><math><mn>0</mn><mo><</mo><mi>θ</mi><mo><</mo><mfrac><mrow><mi>α</mi></mrow><mrow><mn>3</mn></mrow></mfrac></math></span>, <span><math><mn>0</mn><mo><</mo><mi>α</mi><mo><</mo><mn>3</mn></math></span>, <span><math><msub><mrow><mi>I</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow></msub></mrow><mrow><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>3</mn><mo>−</mo><mi>α</mi></mrow></msup></mrow></mfrac></math></span> is the Riesz potential, and <span><math><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> is a positive, asymptotically constant potential. This formulation simultaneously captures <em>Kirchhoff-type nonlocality</em> through the energy-dependent coefficient of the Laplacian, and <em>Choquard criticality</em> via a convolution nonlinearity with critical exponent <span><math><mi>q</mi><mo>=</mo><mn>3</mn><mo>+</mo><mi>α</mi></math></span>.</div><div>By combining variational methods, Pohožaev-type identities, and global compactness techniques adapted to this doubly nonlocal setting, we prove the existence of positive ground state solutions in both subcritical and critical cases. Moreover, we analyze the asymptotic behavior as the nonlocal parameters approach their critical limits, <span><math><mi>θ</mi><mo>→</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>−</mo></mrow></msup></math></span> and <span><math><mi>α</
研究了一类非线性非局部问题,该问题综合了两种复杂机制:kirchhoff型非局部扩散和涉及Hardy-Littlewood-Sobolev (HLS)临界指数的choquard型临界卷积非线性。具体地说,我们考虑R3中的下列方程:−(a+b(∫R3|∇u|2dx)θ)Δu+V(x)u=(Iα α| u|q)|u|q−2u,u∈H1(R3),u>0,其中a,b> 0,0 <θ<α 3,0 <α<3, Iα(x)= a α|x|3−α是Riesz势,V(x)是一个正的渐近常数势。该公式同时通过拉普拉斯函数的能量依赖系数捕获kirchhoff型非局域性,并通过具有临界指数q=3+α的卷积非线性捕获Choquard临界性。通过结合变分方法、Pohožaev-type恒等式和适应于这种双重非局部设置的全局紧性技术,我们证明了在亚临界和临界情况下正基态解的存在性。此外,我们分析了非局部参数逼近临界极限θ→1−和α→3−时的渐近行为,并证明了具有临界幂非线性的极限Kirchhoff方程的收敛性。我们的研究结果强调了Kirchhoff非局域性和Choquard临界性之间丰富的相互作用,揭示了它们在空间可变势的调制下的组合如何引起分析挑战和现象。
{"title":"Ground state solutions and asymptotic behavior for a nonlocal Kirchhoff–Choquard equation with variable potential in R3","authors":"Mohammad Saeid Abolhassanifar ,&nbsp;Reza Saadati ,&nbsp;Mohammad Bagher Ghaemi ,&nbsp;Donal O'Regan","doi":"10.1016/j.jmaa.2026.130445","DOIUrl":"10.1016/j.jmaa.2026.130445","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We investigate a class of nonlinear nonlocal problems that integrate two complex mechanisms: Kirchhoff-type nonlocal diffusion and Choquard-type critical convolution nonlinearity involving the Hardy–Littlewood–Sobolev (HLS) critical exponent. Specifically, we consider the following equation in &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;:&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt; is the Riesz potential, and &lt;span&gt;&lt;math&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is a positive, asymptotically constant potential. This formulation simultaneously captures &lt;em&gt;Kirchhoff-type nonlocality&lt;/em&gt; through the energy-dependent coefficient of the Laplacian, and &lt;em&gt;Choquard criticality&lt;/em&gt; via a convolution nonlinearity with critical exponent &lt;span&gt;&lt;math&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;.&lt;/div&gt;&lt;div&gt;By combining variational methods, Pohožaev-type identities, and global compactness techniques adapted to this doubly nonlocal setting, we prove the existence of positive ground state solutions in both subcritical and critical cases. Moreover, we analyze the asymptotic behavior as the nonlocal parameters approach their critical limits, &lt;span&gt;&lt;math&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;α&lt;/","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130445"},"PeriodicalIF":1.2,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146081414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic behaviour of the heat equation in an exterior domain with general boundary conditions II. The case of bounded and of Lp data 具有一般边界条件的外域热方程的渐近行为[j]。有界和Lp数据的情况
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2026-01-20 DOI: 10.1016/j.jmaa.2026.130448
Joaquín Domínguez-de-Tena , Aníbal Rodríguez-Bernal
In this work, we study the asymptotic behaviour of solutions to the heat equation in exterior domains, i.e., domains which are the complement of a smooth compact set in RN. Different homogeneous boundary conditions are considered, including Dirichlet, Robin, and Neumann ones. In this second part of our work, for N3, we consider the case of bounded initial data and prove that, after some correction term, the solutions become close to the solutions in the whole space and show how complex behaviours appear. We also analyse the case of initial data in Lp with 1<p< where all solutions essentially decay to 0 and the convergence rate could be arbitrarily slow.
在这项工作中,我们研究了热方程的解在外部域的渐近行为,即域是RN中光滑紧集的补。考虑了不同的齐次边界条件,包括Dirichlet、Robin和Neumann边界条件。在第二部分的工作中,对于N≥3,我们考虑了有界初始数据的情况,并证明了经过一些修正项后,解在整个空间中变得接近解,并显示了复杂的行为是如何出现的。我们还分析了Lp中具有1<;p<;∞的初始数据的情况,其中所有解本质上都衰减到0,并且收敛速度可以任意慢。
{"title":"Asymptotic behaviour of the heat equation in an exterior domain with general boundary conditions II. The case of bounded and of Lp data","authors":"Joaquín Domínguez-de-Tena ,&nbsp;Aníbal Rodríguez-Bernal","doi":"10.1016/j.jmaa.2026.130448","DOIUrl":"10.1016/j.jmaa.2026.130448","url":null,"abstract":"<div><div>In this work, we study the asymptotic behaviour of solutions to the heat equation in exterior domains, i.e., domains which are the complement of a smooth compact set in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>. Different homogeneous boundary conditions are considered, including Dirichlet, Robin, and Neumann ones. In this second part of our work, for <span><math><mi>N</mi><mo>≥</mo><mn>3</mn></math></span>, we consider the case of bounded initial data and prove that, after some correction term, the solutions become close to the solutions in the whole space and show how complex behaviours appear. We also analyse the case of initial data in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> with <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mo>∞</mo></math></span> where all solutions essentially decay to 0 and the convergence rate could be arbitrarily slow.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130448"},"PeriodicalIF":1.2,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Volume preserving Willmore flow in a generalized Cahn-Hilliard flow 广义Cahn-Hilliard流中的体积保持Willmore流
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2026-01-20 DOI: 10.1016/j.jmaa.2026.130451
Yuan Chen
We investigate the mass-preserving L2-gradient flow associated with a generalized Cahn–Hilliard equation. Our focus is on the sharp interface regime, where the interface width parameter ε>0 is small. For well-prepared initial data, we rigorously prove that, as ε0, solutions of the diffuse-interface model converge to the volume-preserving Willmore flow in arbitrary spatial dimensions N2. The proof incorporates matched asymptotic expansions, spectrum and energy estimates to establish the convergence of the order parameter away from the interface, alongside a precise motion law derivation for the limiting interface. This result extends the analysis of Fei and Liu [16] from two- and three-dimensional settings to general N-dimensional domains, and it applies to a broad class of symmetric double-well potentials beyond the classical quartic form.
我们研究了与广义Cahn-Hilliard方程相关的保质量l2梯度流。我们的重点是尖锐界面区,其中界面宽度参数ε>;0很小。对于准备充分的初始数据,我们严格证明了当ε→0时,扩散界面模型的解收敛于任意空间维度N≥2的保体积Willmore流。该证明结合了匹配的渐近展开,频谱和能量估计,以建立远离界面的阶参数的收敛性,以及极限界面的精确运动律推导。这一结果将Fei和Liu[16]的分析从二维和三维环境扩展到一般的n维域,并适用于超越经典四次形式的广义对称双井势。
{"title":"Volume preserving Willmore flow in a generalized Cahn-Hilliard flow","authors":"Yuan Chen","doi":"10.1016/j.jmaa.2026.130451","DOIUrl":"10.1016/j.jmaa.2026.130451","url":null,"abstract":"<div><div>We investigate the mass-preserving <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-gradient flow associated with a generalized Cahn–Hilliard equation. Our focus is on the sharp interface regime, where the interface width parameter <span><math><mi>ε</mi><mo>&gt;</mo><mn>0</mn></math></span> is small. For well-prepared initial data, we rigorously prove that, as <span><math><mi>ε</mi><mo>→</mo><mn>0</mn></math></span>, solutions of the diffuse-interface model converge to the <em>volume-preserving Willmore flow</em> in arbitrary spatial dimensions <span><math><mi>N</mi><mo>≥</mo><mn>2</mn></math></span>. The proof incorporates matched asymptotic expansions, spectrum and energy estimates to establish the convergence of the order parameter away from the interface, alongside a precise motion law derivation for the limiting interface. This result extends the analysis of Fei and Liu <span><span>[16]</span></span> from two- and three-dimensional settings to general <em>N</em>-dimensional domains, and it applies to a broad class of symmetric double-well potentials beyond the classical quartic form.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 2","pages":"Article 130451"},"PeriodicalIF":1.2,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Integral representation for a product of two Jacobi functions of the second kind 两个第二类雅可比函数积的积分表示
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2026-01-20 DOI: 10.1016/j.jmaa.2026.130450
Howard S. Cohl , Loyal Durand
By starting with Durand's double integral representation for a product of two Jacobi functions of the second kind, we derive an integral representation for a product of two Jacobi functions of the second kind in kernel form. We also derive a Bateman-type sum for a product of two Jacobi functions of the second kind. From this integral representation we derive integral representations for the Jacobi function of the first kind in both the hyperbolic and trigonometric contexts. From the integral representations for Jacobi functions, we also derive integral representations for products of limiting functions such as associated Legendre functions of the first and second kind, Ferrers functions and also Gegenbauer functions of the first and second kind. By examining the behavior of one of these products near singularities of the relevant functions, we also derive integral representations for single functions, including a Laplace-type integral representation for the Jacobi function of the second kind. Finally, we use the product formulas for the functions of the second kind to derive Nicholson-type integral relations for the sums of squares of Jacobi functions of the first and second kinds, and in a confluent limit, Laguerre functions of the first and second kinds, which generalize the relation eixeix=1 to those functions.
从两个第二类雅可比函数乘积的Durand二重积分表示出发,导出了两个第二类雅可比函数乘积的核形式的积分表示。我们还导出了两个第二类雅可比函数的乘积的bateman型和。从这个积分表示导出了第一类雅可比函数在双曲和三角两种情况下的积分表示。在Jacobi函数的积分表示的基础上,我们还推导了一类和二类相关的Legendre函数、一类和二类相关的Ferrers函数以及一类和二类的Gegenbauer函数等极限函数积的积分表示。通过研究其中一个乘积在相关函数的奇异点附近的行为,我们也推导出单个函数的积分表示,包括第二类Jacobi函数的拉普拉斯型积分表示。最后,利用第二类函数的积公式导出了第一类和第二类Jacobi函数的平方和的nicholson型积分关系,并在合流极限下导出了第一类和第二类lagerre函数,将等式eixe−ix=1推广到这类函数。
{"title":"Integral representation for a product of two Jacobi functions of the second kind","authors":"Howard S. Cohl ,&nbsp;Loyal Durand","doi":"10.1016/j.jmaa.2026.130450","DOIUrl":"10.1016/j.jmaa.2026.130450","url":null,"abstract":"<div><div>By starting with Durand's double integral representation for a product of two Jacobi functions of the second kind, we derive an integral representation for a product of two Jacobi functions of the second kind in kernel form. We also derive a Bateman-type sum for a product of two Jacobi functions of the second kind. From this integral representation we derive integral representations for the Jacobi function of the first kind in both the hyperbolic and trigonometric contexts. From the integral representations for Jacobi functions, we also derive integral representations for products of limiting functions such as associated Legendre functions of the first and second kind, Ferrers functions and also Gegenbauer functions of the first and second kind. By examining the behavior of one of these products near singularities of the relevant functions, we also derive integral representations for single functions, including a Laplace-type integral representation for the Jacobi function of the second kind. Finally, we use the product formulas for the functions of the second kind to derive Nicholson-type integral relations for the sums of squares of Jacobi functions of the first and second kinds, and in a confluent limit, Laguerre functions of the first and second kinds, which generalize the relation <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mi>x</mi></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>i</mi><mi>x</mi></mrow></msup><mo>=</mo><mn>1</mn></math></span> to those functions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130450"},"PeriodicalIF":1.2,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Kirchhoff-type equations involving the fractional (p,q)-Laplacian 涉及分数(p,q)-拉普拉斯式的kirchhoff型方程
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2026-01-20 DOI: 10.1016/j.jmaa.2026.130449
Lisbeth Carrero, Pedro Hernández-Llanos
<div><div>In this paper, we study the existence and nonexistence of solutions for the following Kirchhoff-type fractional <span><math><mo>(</mo><mi>p</mi><mtext>-</mtext><mi>q</mi><mo>)</mo></math></span>-Laplacian problem:<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mi>M</mi><mrow><mo>(</mo><msubsup><mrow><mo>[</mo><mi>u</mi><mo>]</mo></mrow><mrow><mi>p</mi><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><mi>p</mi></mrow></msubsup><mo>)</mo></mrow><msubsup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msubsup><mi>u</mi><mo>+</mo><mi>M</mi><mrow><mo>(</mo><msubsup><mrow><mo>[</mo><mi>u</mi><mo>]</mo></mrow><mrow><mi>q</mi><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mrow><mi>q</mi></mrow></msubsup><mo>)</mo></mrow><msubsup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>q</mi></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msubsup><mi>u</mi></mtd><mtd></mtd></mtr><mtr><mtd><mspace></mspace><mo>=</mo><mi>λ</mi><mo>[</mo><mi>a</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mi>b</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>]</mo><mo>+</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo></mtd><mtd><mtext>in </mtext><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo></mtd><mtd><mtext>on </mtext><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>∖</mo><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> where <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> (<span><math><mi>N</mi><mo>≥</mo><mn>1</mn></math></span>) is a bounded domain with smooth boundary, <span><math><mn>0</mn><mo><</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo><</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub><mo><</mo><mn>1</mn></math></span>, and <span><math><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>p</mi><mo><</mo><mi>N</mi></math></span>. We assume <span><math><mn>1</mn><mo><</mo><mi>q</mi><mo>≤</mo><mi>p</mi><mo><</mo><mi>θ</mi><mi>p</mi><mo><</mo><msubsup><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>:</mo><mo>=</mo><mfrac><mrow><mi>N</mi><mi>p</mi></mrow><mrow><mi>N</mi><mo>−</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>p</mi></mrow></mfrac></math></span>, and <span><math><mi>λ</mi><mo>∈</mo><mi>R</mi></math></span>. The functions <span><math><mi>a</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>b</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>
本文研究了下列kirchhofftype分数型(p-q)- laplace问题解的存在性和不存在性:{M([u]p,s1p)(−Δ)ps1u+M([u]q,s2q)(−Δ)qs2u=λ[a(x)|u|p−2u+b(x)|u|q−2u]+h(x),在Ω,u=0中,在RN∈Ω上,其中Ω∧RN (N≥1)是光滑边界0<;s1<s2<;1和s1p<;N的有界区域。我们假设1 & lt; q≤术;θ术;ps1⁎:= NpN型−s1p,和λ∈R。函数a(x)、b(x)、h(x)是非负的,且a,b∈L∞(Ω), h∈Lq(Ω)。利用变分方法,证明了至少两个弱解的存在性。第一个解是通过直接最小化相关能量泛函得到的,第二个解是通过应用山口定理得到的。我们还证明了参数λ>;0小值时的不存在性。
{"title":"Kirchhoff-type equations involving the fractional (p,q)-Laplacian","authors":"Lisbeth Carrero,&nbsp;Pedro Hernández-Llanos","doi":"10.1016/j.jmaa.2026.130449","DOIUrl":"10.1016/j.jmaa.2026.130449","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper, we study the existence and nonexistence of solutions for the following Kirchhoff-type fractional &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mtext&gt;-&lt;/mtext&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;-Laplacian problem:&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mtext&gt;in &lt;/mtext&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mtext&gt;on &lt;/mtext&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;∖&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;⊂&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; (&lt;span&gt;&lt;math&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;) is a bounded domain with smooth boundary, &lt;span&gt;&lt;math&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. We assume &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. The functions &lt;span&gt;&lt;math&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 2","pages":"Article 130449"},"PeriodicalIF":1.2,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weak type (1,1) bounds for singular integrals with rough kernels on block spaces 块空间上粗糙核奇异积分的弱类型(1,1)界
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2026-01-20 DOI: 10.1016/j.jmaa.2026.130447
Yanping Chen , Teng Wang , Huoxiong Wu
Let ΩL1(Sn1) be a homogeneous function of degree zero and have mean value zero. Consider the rough singular integralTΩf(x)=p.v.RnΩ(xy)|xy|nf(y)dy. We prove that TΩ is of weak type (1,1) if the rough kernel function Ω belongs to the block space Bq0,0(Sn1) for some q>1. This result substantially extends a classical theorem of Seeger (1996) [19].
设Ω∈L1(Sn−1)为0次齐次函数,均值为0。考虑粗糙奇异integralTΩf(x)=p.v.∫RnΩ(x−y)|x−y|nf(y)dy。如果粗糙核函数Ω对某些q>;1属于块空间Bq0,0(Sn−1),则证明TΩ是弱类型(1,1)。这一结果实质上扩展了Seeger(1996)的一个经典定理。
{"title":"Weak type (1,1) bounds for singular integrals with rough kernels on block spaces","authors":"Yanping Chen ,&nbsp;Teng Wang ,&nbsp;Huoxiong Wu","doi":"10.1016/j.jmaa.2026.130447","DOIUrl":"10.1016/j.jmaa.2026.130447","url":null,"abstract":"<div><div>Let <span><math><mi>Ω</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></math></span> be a homogeneous function of degree zero and have mean value zero. Consider the rough singular integral<span><span><span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>Ω</mi></mrow></msub><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mrow><mi>p</mi><mo>.</mo><mi>v</mi><mo>.</mo></mrow><munder><mo>∫</mo><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></munder><mfrac><mrow><mi>Ω</mi><mo>(</mo><mi>x</mi><mo>−</mo><mi>y</mi><mo>)</mo></mrow><mrow><mo>|</mo><mi>x</mi><mo>−</mo><mi>y</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>n</mi></mrow></msup></mrow></mfrac><mi>f</mi><mo>(</mo><mi>y</mi><mo>)</mo><mi>d</mi><mi>y</mi><mo>.</mo></math></span></span></span> We prove that <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>Ω</mi></mrow></msub></math></span> is of weak type <span><math><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> if the rough kernel function Ω belongs to the block space <span><math><msubsup><mrow><mi>B</mi></mrow><mrow><mi>q</mi></mrow><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></msubsup><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></math></span> for some <span><math><mi>q</mi><mo>&gt;</mo><mn>1</mn></math></span>. This result substantially extends a classical theorem of Seeger (1996) <span><span>[19]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130447"},"PeriodicalIF":1.2,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global positive bounded solutions for equations with regularly varying operator 正则变算子方程的整体正有界解
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2026-01-19 DOI: 10.1016/j.jmaa.2026.130443
Zuzana Došlá , Mauro Marini , Serena Matucci
A nonlinear differential equation with inhomogeneous differential operator Φ, which is regularly varying at zero, is considered. The operator Φ can be viewed as an extension of the p-Laplacian operator and arises in many physical problems, as illustrated by several examples. In particular, the existence of global positive bounded solutions on the half-line with the Neumann type boundary conditions is studied by means of an abstract fixed point theorem and certain properties of an associated half-linear equation. The results do not require the explicit form of the inverse operator of Φ, and are completed by an asymptotic analysis of these solutions near infinity.
考虑了在零处有规则变化的非齐次微分算子Φ非线性微分方程。算符Φ可以看作是p-拉普拉斯算符的扩展,在许多物理问题中出现,如几个例子所示。特别地,利用抽象不动点定理和相关半线性方程的某些性质,研究了具有Neumann型边界条件的半线上整体正有界解的存在性。结果不需要Φ逆算子的显式形式,并通过对这些解在无穷远处的渐近分析来完成。
{"title":"Global positive bounded solutions for equations with regularly varying operator","authors":"Zuzana Došlá ,&nbsp;Mauro Marini ,&nbsp;Serena Matucci","doi":"10.1016/j.jmaa.2026.130443","DOIUrl":"10.1016/j.jmaa.2026.130443","url":null,"abstract":"<div><div>A nonlinear differential equation with inhomogeneous differential operator Φ, which is regularly varying at zero, is considered. The operator Φ can be viewed as an extension of the <em>p</em>-Laplacian operator and arises in many physical problems, as illustrated by several examples. In particular, the existence of global positive bounded solutions on the half-line with the Neumann type boundary conditions is studied by means of an abstract fixed point theorem and certain properties of an associated half-linear equation. The results do not require the explicit form of the inverse operator of Φ, and are completed by an asymptotic analysis of these solutions near infinity.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130443"},"PeriodicalIF":1.2,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A porous medium equation with spatially inhomogeneous absorption. Part II: Large time behavior 具有空间非均匀吸收的多孔介质方程。第二部分:大时间行为
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2026-01-19 DOI: 10.1016/j.jmaa.2026.130444
Razvan Gabriel Iagar , Diana-Rodica Munteanu
<div><div>We study the large time behavior of solutions to the Cauchy problem for the quasilinear absorption-diffusion equation<span><span><span><math><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>=</mo><mi>Δ</mi><msup><mrow><mi>u</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>−</mo><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>σ</mi></mrow></msup><msup><mrow><mi>u</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>,</mo><mspace></mspace><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>,</mo></math></span></span></span> with exponents <span><math><mi>p</mi><mo>></mo><mi>m</mi><mo>></mo><mn>1</mn></math></span> and <span><math><mi>σ</mi><mo>></mo><mn>0</mn></math></span> and with initial conditions either satisfying<span><span><span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>)</mo><mo>∩</mo><mi>C</mi><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>)</mo><mo>,</mo><mspace></mspace><munder><mi>lim</mi><mrow><mo>|</mo><mi>x</mi><mo>|</mo><mo>→</mo><mo>∞</mo></mrow></munder><mo>⁡</mo><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>θ</mi></mrow></msup><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>A</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span></span></span> for some <span><math><mi>θ</mi><mo>≥</mo><mn>0</mn></math></span>. A number of different asymptotic profiles are identified, and uniform convergence on time-expanding sets towards them is established, according to the position of both <em>p</em> and <em>θ</em> with respect to the following critical exponents<span><span><span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>F</mi></mrow></msub><mo>(</mo><mi>σ</mi><mo>)</mo><mo>=</mo><mi>m</mi><mo>+</mo><mfrac><mrow><mi>σ</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>N</mi></mrow></mfrac><mo>,</mo><mspace></mspace><msub><mrow><mi>θ</mi></mrow><mrow><mo>⁎</mo></mrow></msub><mo>=</mo><mfrac><mrow><mi>σ</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>p</mi><mo>−</mo><mi>m</mi></mrow></mfrac><mo>,</mo><mspace></mspace><msup><mrow><mi>θ</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>=</mo><mi>N</mi><mo>.</mo></math></span></span></span> More precisely, solutions in radially symmetric self-similar form decaying as <span><math><mo>|</mo><mi>x</mi><mo>|</mo><mo>→</mo><mo>∞</mo></math></span> with the rates<span><span><span><math><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∼</mo><mi>A</mi><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mo>−</mo><msub><mrow><mi>θ</mi></mrow><mrow><mo>⁎</mo></mrow></msub></mrow></msup><mo>,</mo><mspace></mspace><mrow><mi>or</mi></mrow><mspace></mspace><mi>u</mi><
我们研究了拟线性吸收扩散方程∂tu=Δum−|x|σup,(x,t)∈rnx(0,∞),指数p>;m>;1和σ>;0,且初始条件满足:0∈L∞(RN)∩C(RN),lim|x| x|θu0(x)=A∈(0,∞),对于某些θ≥0。根据p和θ相对于下列临界指数的位置:spf (σ)=m+σ+2N,θ =σ+2p−m,θ =N,确定了若干不同的渐近曲线,并建立了它们在时间扩展集上的一致收敛性。更准确地说,在某些情况下,我们得到了衰减为|x|→∞,速率为u(x,t) ~ A|x|−θ β,oru(x,t) ~ (1p−1)1/(p−1)|x|−σ/(p−1)的径向对称自相似形式的解,而在其他情况下也出现了时间尺度上的渐近简化或对数修正。其中一些自相似解的唯一性,在本工作的第一部分被搁置,也被建立。
{"title":"A porous medium equation with spatially inhomogeneous absorption. Part II: Large time behavior","authors":"Razvan Gabriel Iagar ,&nbsp;Diana-Rodica Munteanu","doi":"10.1016/j.jmaa.2026.130444","DOIUrl":"10.1016/j.jmaa.2026.130444","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We study the large time behavior of solutions to the Cauchy problem for the quasilinear absorption-diffusion equation&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; with exponents &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; and with initial conditions either satisfying&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∩&lt;/mo&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;munder&gt;&lt;mi&gt;lim&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; for some &lt;span&gt;&lt;math&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. A number of different asymptotic profiles are identified, and uniform convergence on time-expanding sets towards them is established, according to the position of both &lt;em&gt;p&lt;/em&gt; and &lt;em&gt;θ&lt;/em&gt; with respect to the following critical exponents&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; More precisely, solutions in radially symmetric self-similar form decaying as &lt;span&gt;&lt;math&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; with the rates&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∼&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mrow&gt;&lt;mi&gt;or&lt;/mi&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 2","pages":"Article 130444"},"PeriodicalIF":1.2,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Upper and lower bounds for the eigenvalues of the clamped plate problem on Riemannian manifolds 黎曼流形上夹紧板问题特征值的上界和下界
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2026-01-16 DOI: 10.1016/j.jmaa.2026.130442
Zhengchao Ji
In this paper, we establish some inequalities for the higher eigenvalues Λi of the clamped plate problem on Riemannian manifolds with bounded sectional curvature. Our proofs are based on a Laplacian comparison and the Fourier transform. As an application of the Laplacian comparison, we obtain a generalized inequality of Cheng-Wei in Rn. We also prove an improved lower bound for ikΛi.
本文建立了有界截面曲率黎曼流形上夹紧板问题的高特征值Λi的一些不等式。我们的证明是基于拉普拉斯比较和傅里叶变换。作为拉普拉斯比较的一个应用,我们得到了Rn中Cheng-Wei的一个广义不等式。我们还证明了∑ikΛi的改进下界。
{"title":"Upper and lower bounds for the eigenvalues of the clamped plate problem on Riemannian manifolds","authors":"Zhengchao Ji","doi":"10.1016/j.jmaa.2026.130442","DOIUrl":"10.1016/j.jmaa.2026.130442","url":null,"abstract":"<div><div>In this paper, we establish some inequalities for the higher eigenvalues <span><math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> of the clamped plate problem on Riemannian manifolds with bounded sectional curvature. Our proofs are based on a Laplacian comparison and the Fourier transform. As an application of the Laplacian comparison, we obtain a generalized inequality of Cheng-Wei in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. We also prove an improved lower bound for <span><math><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi></mrow><mrow><mi>k</mi></mrow></msubsup><msub><mrow><mi>Λ</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130442"},"PeriodicalIF":1.2,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
期刊
Journal of Mathematical Analysis and Applications
全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1