Journal of Mathematical Analysis and Applications最新文献

{"title":"Analytical solutions and asymptotic profiles of vacuum free boundary for the compressible Euler equations with time-dependent damping","authors":"Kunquan Li ,&nbsp;Jia Jia ,&nbsp;Meng Zhang ,&nbsp;Zhengguang Guo","doi":"10.1016/j.jmaa.2025.129340","DOIUrl":"10.1016/j.jmaa.2025.129340","url":null,"abstract":"<div><div>We constructed a class of analytical, rotational and self-similar solutions to the isentropic compressible Euler equations with time-dependent damping <span><math><mfrac><mrow><mi>μ</mi></mrow><mrow><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>t</mi><mo>)</mo></mrow><mrow><mi>λ</mi></mrow></msup></mrow></mfrac><mi>ρ</mi><mi>u</mi></math></span> (<span><math><mi>μ</mi><mo>≥</mo><mn>0</mn></math></span>, <span><math><mi>λ</mi><mo>∈</mo><mi>R</mi></math></span>) and vacuum free boundary in cylindrical coordinates. These solutions indicate the fact that the sound speed is <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></span>-Hölder continuous across the boundary (i.e., the physical vacuum) and is determined by the free boundary <span><math><mi>a</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span>, which is the solution of a second order nonlinear ordinary differential equation with parameters <em>μ</em> and <em>λ</em> (see <span><span>(1.12)</span></span>). The global existence and detailed spreading rate of the free boundary <span><math><mi>a</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span> are presented, while the stability for the free boundary problem is still unknown. Precisely, we show that for <span><math><mi>λ</mi><mo>&gt;</mo><mn>1</mn></math></span> the free boundary will grow linearly in time, and radial velocity <span><math><msup><mrow><mi>u</mi></mrow><mrow><mi>r</mi></mrow></msup></math></span> and axial velocity <span><math><msup><mrow><mi>u</mi></mrow><mrow><mi>z</mi></mrow></msup></math></span> are bounded, while the angular velocity <span><math><msup><mrow><mi>u</mi></mrow><mrow><mi>ϕ</mi></mrow></msup></math></span> and the radial derivatives of velocity components all tend to zero as <span><math><mi>t</mi><mo>→</mo><mo>+</mo><mo>∞</mo></math></span> (see <span><span>Remark 1.6</span></span>). However, if <span><math><mi>λ</mi><mo>≤</mo><mn>1</mn></math></span>, the free boundary will grow sub-linearly in time. In particular, if <span><math><mo>−</mo><mn>1</mn><mo>≤</mo><mi>λ</mi><mo>≤</mo><mn>1</mn><mo>/</mo><mo>(</mo><mn>2</mn><mi>γ</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>, where <em>γ</em> is the adiabatic exponent of polytropic gases, the free boundary will grow more slowly as <em>λ</em> becomes smaller, and possesses a finite upper bound when <span><math><mi>λ</mi><mo>&lt;</mo><mo>−</mo><mn>1</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 2","pages":"Article 129340"},"PeriodicalIF":1.2,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143394390","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}

{"title":"Global boundedness of Lotka-Volterra competition system with cross-diffusion","authors":"Dongze Yan","doi":"10.1016/j.jmaa.2025.129346","DOIUrl":"10.1016/j.jmaa.2025.129346","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper, we consider the following Lotka-Volterra competition system with cross-diffusion&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;α&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;Δ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&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;/msub&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;β&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;Δ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&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;/msub&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; under homogeneous Neumann boundary conditions in a smooth bounded domain &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;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; (&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; depend on the initial data &lt;em&gt;w&lt;/em&gt;). It is shown that the problem possesses a global classical solution for &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;. On the other hand, in the case &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, it is proved the global existence of classical solutions for &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/m","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 2","pages":"Article 129346"},"PeriodicalIF":1.2,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143348579","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}

{"title":"Positivity-preserving numerical scheme for the alpha-constant elasticity of variance process","authors":"Libo Li,&nbsp;Guanting Liu","doi":"10.1016/j.jmaa.2025.129341","DOIUrl":"10.1016/j.jmaa.2025.129341","url":null,"abstract":"<div><div>In this article, we present a method for constructing a positivity-preserving numerical scheme for a jump-extended constant elasticity of variance (CEV) process, where jumps are governed by a spectrally positive <em>α</em>-stable process with <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>. The numerical scheme is obtained by making the diffusion coefficient <span><math><msup><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msup></math></span>, where <span><math><mi>γ</mi><mo>∈</mo><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mn>1</mn><mo>)</mo></math></span>, partially implicit and then finding the appropriate adjustment factor. We show that for a sufficiently small step size, the proposed scheme converges and theoretically achieves a strong convergence rate of at least <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mrow><mo>(</mo><mfrac><mrow><msub><mrow><mi>α</mi></mrow><mrow><mo>−</mo></mrow></msub></mrow><mrow><mn>2</mn></mrow></mfrac><mo>∧</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>α</mi></mrow></mfrac><mo>∧</mo><mi>ρ</mi><mo>)</mo></mrow></math></span>, where <span><math><mi>ρ</mi><mo>∈</mo><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mn>1</mn><mo>)</mo></math></span> is the Hölder exponent of the jump coefficient <span><math><msup><mrow><mi>x</mi></mrow><mrow><mi>ρ</mi></mrow></msup></math></span> and the constant <span><math><msub><mrow><mi>α</mi></mrow><mrow><mo>−</mo></mrow></msub><mo>&lt;</mo><mi>α</mi></math></span> can be chosen as arbitrarily close to <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 2","pages":"Article 129341"},"PeriodicalIF":1.2,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Best constants in reverse Riesz-type inequalities for analytic and co-analytic projections","authors":"Petar Melentijević","doi":"10.1016/j.jmaa.2025.129336","DOIUrl":"10.1016/j.jmaa.2025.129336","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mi>P</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span> be the Riesz's projection operator and let <span><math><msub><mrow><mi>P</mi></mrow><mrow><mo>−</mo></mrow></msub><mo>=</mo><mi>I</mi><mo>−</mo><msub><mrow><mi>P</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span>. We consider the inequalities of the following form:<span><span><span><math><msub><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>T</mi><mo>)</mo></mrow></msub><mo>≤</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>s</mi></mrow></msub><msub><mrow><mo>‖</mo><msup><mrow><mo>(</mo><mo>|</mo><msub><mrow><mi>P</mi></mrow><mrow><mo>+</mo></mrow></msub><mi>f</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>s</mi></mrow></msup><mo>+</mo><mo>|</mo><msub><mrow><mi>P</mi></mrow><mrow><mo>−</mo></mrow></msub><mi>f</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>s</mi></mrow></msup><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>s</mi></mrow></mfrac></mrow></msup><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>T</mi><mo>)</mo></mrow></msub></math></span></span></span> and prove them with sharp constant <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>s</mi></mrow></msub></math></span> for <span><math><mi>s</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo><mo>∪</mo><mo>[</mo><msup><mrow><mi>p</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>,</mo><mo>+</mo><mo>∞</mo><mo>)</mo></math></span> and <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>≤</mo><mn>2</mn></math></span> or <span><math><mi>p</mi><mo>≥</mo><mn>4</mn></math></span>, where <span><math><msup><mrow><mi>p</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>:</mo><mo>=</mo><mi>min</mi><mo>⁡</mo><mo>{</mo><mi>p</mi><mo>,</mo><mfrac><mrow><mi>p</mi></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mo>}</mo></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 2","pages":"Article 129336"},"PeriodicalIF":1.2,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143394962","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}

{"title":"Exact solutions for nonlinear trapped lee waves in the β-plane approximation","authors":"Lili Fan,&nbsp;Ruonan Liu,&nbsp;Heyang Li","doi":"10.1016/j.jmaa.2025.129337","DOIUrl":"10.1016/j.jmaa.2025.129337","url":null,"abstract":"<div><div>In this paper, we construct exact solutions that character three-dimensional, nonlinear trapped lee wave propagation superimposed on longitudinal atmospheric currents in the <em>β</em>-plane approximation. The solutions obtained are presented in Lagrangian coordinates, and are Gerstner-like solutions. In the process, we also derive the dispersion relation and analyze the density, pressure and the vorticity qualitatively.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 2","pages":"Article 129337"},"PeriodicalIF":1.2,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143271436","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}

{"title":"On a sign-change conjecture of Schlosser and Zhou","authors":"Kathrin Bringmann ,&nbsp;Bernhard Heim ,&nbsp;Ben Kane","doi":"10.1016/j.jmaa.2025.129339","DOIUrl":"10.1016/j.jmaa.2025.129339","url":null,"abstract":"<div><div>In this paper, we investigate the sign changes of Fourier coefficients of infinite products of <em>q</em>-series of Rogers–Ramanujan type. In particular, we prove a conjecture made by Schlosser–Zhou pertaining to such sign changes for products of modulus 10.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"548 2","pages":"Article 129339"},"PeriodicalIF":1.2,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510521","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}

{"title":"A class of C-normal weighted composition operators on quaternionic Fock space","authors":"Guiquan Liang,&nbsp;Yuxia Liang","doi":"10.1016/j.jmaa.2025.129338","DOIUrl":"10.1016/j.jmaa.2025.129338","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>ψ</mi><mo>,</mo><mi>φ</mi></mrow></msub></math></span> be the bounded weighted composition operator on quaternionic Fock space <span><math><msup><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>H</mi><mo>)</mo></math></span> with <span><math><mi>φ</mi><mo>(</mo><mi>p</mi><mo>)</mo><mo>=</mo><mi>p</mi><mi>a</mi><mo>+</mo><mi>b</mi></math></span> and slice regular function <em>ψ</em> on <span><math><mi>H</mi></math></span>. We mainly explore the prerequisites for <span><math><mi>C</mi></math></span>-normal and <span><math><mi>C</mi></math></span>-symmetric <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>ψ</mi><mo>,</mo><mi>φ</mi></mrow></msub></math></span> under <span><math><mo>|</mo><mi>a</mi><mo>|</mo><mo>≤</mo><mn>1</mn></math></span>. We further describe the <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>s</mi><mo>,</mo><mi>t</mi></mrow></msub></math></span>-normal <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>ψ</mi><mo>,</mo><mi>φ</mi></mrow></msub></math></span> and exhibit two examples for binormal weighted composition operator, extending the results on complex Fock space.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"546 2","pages":"Article 129338"},"PeriodicalIF":1.2,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143421647","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}

{"title":"Pullback exponential attractor of dynamical systems associated with non-cylindrical problems","authors":"Jackeline Huaccha Neyra ,&nbsp;Heraclio López-Lázaro ,&nbsp;Obidio Rubio ,&nbsp;Carlos R. Takaessu Junior","doi":"10.1016/j.jmaa.2025.129332","DOIUrl":"10.1016/j.jmaa.2025.129332","url":null,"abstract":"<div><div>In this work, we present a way of approaching the theory of pullback exponential attractors for dynamical systems on time-dependent phase spaces (or dynamical systems associated with non-cylindrical problems). We will show that these types of dynamical systems satisfying the smoothing property have a pullback exponential attractor, extending the results for dynamical systems defined on a fixed phase space, e.g. <span><span>[5]</span></span>, <span><span>[15]</span></span>, <span><span>[25]</span></span>. Furthermore, we will apply this theory to show that the dynamical system associated with the 2D-Navier-Stokes equations on some non-cylindrical domain has a pullback exponential attractor on a suitable tempered universe that depends on the time integrability of the external force and the behavior of the initial conditions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 2","pages":"Article 129332"},"PeriodicalIF":1.2,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161335","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}

{"title":"Stability of limit expansive systems","authors":"Ngocthach Nguyen","doi":"10.1016/j.jmaa.2025.129335","DOIUrl":"10.1016/j.jmaa.2025.129335","url":null,"abstract":"<div><div>In this paper, we study the stability of limit expansive systems. More precisely, we prove that if a homeomorphism on a compact metric space is limit expansive and has the shadowing property, then it is topologically Ω-stable. Moreover, a circle homeomorphism is topologically stable if and only if it is limit expansive and has the shadowing property. Furthermore, we show that if a linear operator on a Banach space is limit expansive and has the shadowing property, then it is topologically stable. For a finite dimensional Banach space, the notion of limit expansiveness and topological stability for linear operators are equivalent. Finally, we characterize the notion of Ω-stability for diffeomorphisms on compact smooth manifolds by using the notion of limit expansiveness.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 2","pages":"Article 129335"},"PeriodicalIF":1.2,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143271435","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}

{"title":"The discrete Lp Minkowski problem for log-capacity for p < 0","authors":"Hui Zeng,&nbsp;Lijuan Liu,&nbsp;Min He","doi":"10.1016/j.jmaa.2025.129334","DOIUrl":"10.1016/j.jmaa.2025.129334","url":null,"abstract":"<div><div>Sufficient condition is given for the existence of solutions to the discrete <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> Minkowski problem for log-capacity for <span><math><mi>p</mi><mo>&lt;</mo><mn>0</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 2","pages":"Article 129334"},"PeriodicalIF":1.2,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143271707","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}