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Analytical solutions and asymptotic profiles of vacuum free boundary for the compressible Euler equations with time-dependent damping
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-05 DOI: 10.1016/j.jmaa.2025.129340
Kunquan Li , Jia Jia , Meng Zhang , Zhengguang Guo
We constructed a class of analytical, rotational and self-similar solutions to the isentropic compressible Euler equations with time-dependent damping μ(1+t)λρu (μ0, λR) and vacuum free boundary in cylindrical coordinates. These solutions indicate the fact that the sound speed is C1/2-Hölder continuous across the boundary (i.e., the physical vacuum) and is determined by the free boundary a(t), which is the solution of a second order nonlinear ordinary differential equation with parameters μ and λ (see (1.12)). The global existence and detailed spreading rate of the free boundary a(t) are presented, while the stability for the free boundary problem is still unknown. Precisely, we show that for λ>1 the free boundary will grow linearly in time, and radial velocity ur and axial velocity uz are bounded, while the angular velocity uϕ and the radial derivatives of velocity components all tend to zero as t+ (see Remark 1.6). However, if λ1, the free boundary will grow sub-linearly in time. In particular, if 1λ1/(2γ1), where γ is the adiabatic exponent of polytropic gases, the free boundary will grow more slowly as λ becomes smaller, and possesses a finite upper bound when λ<1.
{"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}
引用次数: 0
Global boundedness of Lotka-Volterra competition system with cross-diffusion
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-05 DOI: 10.1016/j.jmaa.2025.129346
Dongze Yan
<div><div>In this paper, we consider the following Lotka-Volterra competition system with cross-diffusion<span><span><span><math><mrow><mrow><mo>{</mo><mtable><mtr><mtd></mtd><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mo>(</mo><mi>ϕ</mi><mo>(</mo><mi>w</mi><mo>)</mo><mi>u</mi><mo>)</mo><mo>+</mo><msub><mrow><mi>α</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>Δ</mi><mo>(</mo><mi>u</mi><mi>v</mi><mo>)</mo><mo>−</mo><msub><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msub><mi>u</mi><mi>v</mi><mo>+</mo><msub><mrow><mi>α</mi></mrow><mrow><mn>3</mn></mrow></msub><mi>u</mi><mi>w</mi><mo>−</mo><msub><mrow><mi>α</mi></mrow><mrow><mn>4</mn></mrow></msub><mi>u</mi><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mo>(</mo><mi>ϕ</mi><mo>(</mo><mi>w</mi><mo>)</mo><mi>v</mi><mo>)</mo><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>Δ</mi><mo>(</mo><mi>u</mi><mi>v</mi><mo>)</mo><mo>−</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msub><mi>u</mi><mi>v</mi><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>3</mn></mrow></msub><mi>v</mi><mi>w</mi><mo>−</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>4</mn></mrow></msub><mi>v</mi><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow><mi>w</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>w</mi><mo>−</mo><mi>u</mi><mi>w</mi><mo>−</mo><mi>v</mi><mi>w</mi><mo>+</mo><msub><mrow><mi>r</mi></mrow><mrow><mn>3</mn></mrow></msub><mi>w</mi><mo>(</mo><mn>1</mn><mo>−</mo><mi>w</mi><mo>)</mo><mo>,</mo></mtd></mtr></mtable></mrow></mrow></math></span></span></span> under homogeneous Neumann boundary conditions in a smooth bounded domain <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mspace></mspace><mo>(</mo><mi>n</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span> with <span><math><msub><mrow><mi>α</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>></mo><msub><mrow><mi>α</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>β</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>></mo><msub><mrow><mi>β</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> (<span><math><msub><mrow><mi>α</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>β</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> depend on the initial data <em>w</em>). It is shown that the problem possesses a global classical solution for <span><math><mi>n</mi><mo>=</mo><mn>1</mn></math></span>. On the other hand, in the case <span><math><mi>n</mi><mo>=</mo><mn>2</mn></math></span>, it is proved the global existence of classical solutions for <span><math><msub><mrow><mi>α</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>β</mi></mrow><mrow><mi>i</mi></mrow></msub><mspace></mspace><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</m
{"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}
引用次数: 0
Positivity-preserving numerical scheme for the alpha-constant elasticity of variance process
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-05 DOI: 10.1016/j.jmaa.2025.129341
Libo Li, Guanting Liu
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 α-stable process with α(1,2). The numerical scheme is obtained by making the diffusion coefficient xγ, where γ(12,1), 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 12(α21αρ), where ρ(12,1) is the Hölder exponent of the jump coefficient xρ and the constant α<α can be chosen as arbitrarily close to α(1,2).
{"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}
引用次数: 0
Best constants in reverse Riesz-type inequalities for analytic and co-analytic projections
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-04 DOI: 10.1016/j.jmaa.2025.129336
Petar Melentijević
Let P+ be the Riesz's projection operator and let P=IP+. We consider the inequalities of the following form:fLp(T)Bp,s(|P+f|s+|Pf|s)1sLp(T) and prove them with sharp constant Bp,s for s(0,1][p,+) and 1<p2 or p4, where p:=min{p,pp1}.
{"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}
引用次数: 0
Exact solutions for nonlinear trapped lee waves in the β-plane approximation
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-04 DOI: 10.1016/j.jmaa.2025.129337
Lili Fan, Ruonan Liu, Heyang Li
In this paper, we construct exact solutions that character three-dimensional, nonlinear trapped lee wave propagation superimposed on longitudinal atmospheric currents in the β-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.
{"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}
引用次数: 0
On a sign-change conjecture of Schlosser and Zhou
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-04 DOI: 10.1016/j.jmaa.2025.129339
Kathrin Bringmann , Bernhard Heim , Ben Kane
In this paper, we investigate the sign changes of Fourier coefficients of infinite products of q-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.
{"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}
引用次数: 0
A class of C-normal weighted composition operators on quaternionic Fock space
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-04 DOI: 10.1016/j.jmaa.2025.129338
Guiquan Liang, Yuxia Liang
Let Wψ,φ be the bounded weighted composition operator on quaternionic Fock space F2(H) with φ(p)=pa+b and slice regular function ψ on H. We mainly explore the prerequisites for C-normal and C-symmetric Wψ,φ under |a|1. We further describe the Cr,s,t-normal Wψ,φ and exhibit two examples for binormal weighted composition operator, extending the results on complex Fock space.
{"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}
引用次数: 0
Pullback exponential attractor of dynamical systems associated with non-cylindrical problems
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-03 DOI: 10.1016/j.jmaa.2025.129332
Jackeline Huaccha Neyra , Heraclio López-Lázaro , Obidio Rubio , Carlos R. Takaessu Junior
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. [5], [15], [25]. 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.
{"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}
引用次数: 0
Stability of limit expansive systems
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-03 DOI: 10.1016/j.jmaa.2025.129335
Ngocthach Nguyen
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.
{"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}
引用次数: 0
The discrete Lp Minkowski problem for log-capacity for p < 0
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-03 DOI: 10.1016/j.jmaa.2025.129334
Hui Zeng, Lijuan Liu, Min He
Sufficient condition is given for the existence of solutions to the discrete Lp Minkowski problem for log-capacity for p<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}
引用次数: 0
期刊
Journal of Mathematical Analysis and Applications
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