Nonlinear Analysis-Real World Applications最新文献

{"title":"Global bounded solution in an attraction repulsion Chemotaxis-Navier-Stokes system with Neumann and Dirichlet boundary conditions","authors":"Luli Xu,&nbsp;Chunlai Mu,&nbsp;Minghua Zhang,&nbsp;Jing Zhang","doi":"10.1016/j.nonrwa.2024.104247","DOIUrl":"10.1016/j.nonrwa.2024.104247","url":null,"abstract":"<div><div>This paper deals with an attraction–repulsion Chemotaxis-Navier–Stokes system with Dirichlet boundary for the attraction signal and Neumann boundary for the repulsion signal. Based on the work of Winkler (2020) and Wang et al. (2022), by using a series estimates, it is shown that in two dimension the classical solution of the system is globally bounded, under the condition of small initial values <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></msub></math></span> in the explicit expressions for <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></msub></math></span> and attraction–repulsion coefficients.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592773","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":"Threshold value for a quasilinear Keller–Segel chemotaxis system with the intermediate exponent in a bounded domain","authors":"Hua Zhong","doi":"10.1016/j.nonrwa.2024.104253","DOIUrl":"10.1016/j.nonrwa.2024.104253","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We consider a quasilinear chemotaxis model &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mtable&gt;&lt;mtr&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;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&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;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;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&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;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;τ&lt;/mi&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;mi&gt;v&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;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; with nonlinear diffusion function &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and chemotactic sensitivity &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; in a bounded domain &lt;span&gt;&lt;math&gt;&lt;mrow&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;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Here the rate &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; grows like &lt;span&gt;&lt;math&gt;&lt;msup&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;mo&gt;−&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; as &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;.&lt;/div&gt;&lt;div&gt;It is first shown that there exists a &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; such that if free energy with initial data is suitably small and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&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;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&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;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&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;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mrow&gt;","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592774","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 Poincaré bifurcation by perturbing a class of cubic Hamiltonian systems","authors":"Yuan Chang,&nbsp;Liqin Zhao,&nbsp;Qiuyi Wang","doi":"10.1016/j.nonrwa.2024.104246","DOIUrl":"10.1016/j.nonrwa.2024.104246","url":null,"abstract":"<div><div>This paper studies the Poincaré bifurcation of the planar vector fields <span><math><mrow><mover><mrow><mi>x</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>y</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow><mo>+</mo><mi>ɛ</mi><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mover><mrow><mi>y</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mo>−</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>x</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow><mo>+</mo><mi>ɛ</mi><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></mrow></math></span>, where <span><math><mrow><mn>0</mn><mo>&lt;</mo><mrow><mo>|</mo><mi>ɛ</mi><mo>|</mo></mrow><mo>≪</mo><mn>1</mn></mrow></math></span>, <span><span><span><math><mrow><mi>H</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow><mo>=</mo><mi>α</mi><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>β</mi><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>a</mi><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>+</mo><mi>b</mi><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>c</mi><msup><mrow><mi>y</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>,</mo><mspace></mspace><mspace></mspace><mspace></mspace><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></mrow><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>5</mn></mrow></msup><mo>,</mo><mspace></mspace><mi>α</mi><mi>β</mi><mo>&lt;</mo><mn>0</mn></mrow></math></span></span></span>with <span><math><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>≠</mo><mn>0</mn></mrow></math></span>, and <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></mrow></math></span> are polynomials in <span><math><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></math></span> of the degree <span><math><mi>n</mi></math></span>. The phase portraits of the unperturbed systems with at least one center can be divided into 10 classes by their phase portraits. For general <span><math><mi>n</mi></math></span>, we obtain the upper bound of the number of limit cycles bifurcating from period annuli if the first order Melnikov function is not identically zero. The results are new and some of the results in the literatures are improved.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587385","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":"Boundedness and stabilization in an indirect pursuit-evasion model with nonlinear signal-dependent diffusion and sensitivity","authors":"Chuanjia Wan,&nbsp;Pan Zheng","doi":"10.1016/j.nonrwa.2024.104234","DOIUrl":"10.1016/j.nonrwa.2024.104234","url":null,"abstract":"&lt;div&gt;&lt;div&gt;This paper deals with an indirect pursuit-evasion model with signal-dependent diffusion and sensitivity &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mfenced&gt;&lt;mrow&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;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&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;mo&gt;(&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mfenced&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;mo&gt;(&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mi&gt;α&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;a&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;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;b&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;u&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&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;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&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;mo&gt;(&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mfenced&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;mo&gt;(&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;a&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;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;b&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;v&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&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;β&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&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;z&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;z&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;under homogeneous Neumann boundary conditions in a smoothly bounded domain &lt;span&gt;&lt;math&gt;&lt;mrow&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;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, where the parameters &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;a&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;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;a&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;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;b&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;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587386","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":"Higher order asymptotic expansions for the convection–diffusion equation in the Fujita-subcritical case","authors":"Ryunosuke Kusaba","doi":"10.1016/j.nonrwa.2024.104249","DOIUrl":"10.1016/j.nonrwa.2024.104249","url":null,"abstract":"<div><div>This paper is devoted to the asymptotic behavior of global solutions to the convection–diffusion equation in the Fujita-subcritical case. We improve the result by Zuazua (1993) and establish higher order asymptotic expansions with decay estimates of the remainders. We also discuss the optimality for the decay rates of the remainders.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587387","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":"On the spectral stability of periodic waves of the dispersive systems of modified KdV equations","authors":"Sevdzhan Hakkaev ,&nbsp;Kadir Şamdanlı","doi":"10.1016/j.nonrwa.2024.104250","DOIUrl":"10.1016/j.nonrwa.2024.104250","url":null,"abstract":"<div><div>This paper concerns the stability of periodic traveling waves of cnoidal type for the nonlinear dispersive systems. The main objective of the paper is to study their stability with respect to co-periodic perturbations.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578777","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":"Large-time behavior of solutions to outflow problem of full compressible Navier–Stokes–Korteweg equations","authors":"Yeping Li,&nbsp;Heyu Liu,&nbsp;Rong Yin","doi":"10.1016/j.nonrwa.2024.104248","DOIUrl":"10.1016/j.nonrwa.2024.104248","url":null,"abstract":"<div><div>In this article, we investigate the large-time behavior of the solution to outflow problem for full compressible Navier–Stokes–Korteweg equations in the one-dimensional half space. The full compressible Navier–Stokes–Korteweg equations model compressible fluids with viscosity, heat-conductivity and internal capillarity, and include the Korteweg stress effects into the dissipative structure of the hyperbolic–parabolic system and turn out to be more complicated than that in the simpler full compressible Navier–Stokes equations. Under some suitable assumptions of the far fields and the boundary values of the density, the velocity and the absolute temperature, the asymptotic stability of the boundary layer, the 3-rarefaction wave, and the superposition of the boundary layer and the 3-rarefaction wave are shown provided that the initial perturbation and the strength of the nonlinear wave are small. The proof is mainly based on <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-energy method, some time-decay estimates of the smoothed rarefaction wave and the space-decay estimates of the boundary layer. This can be viewed as the first result about the stability of basic wave patterns for the outflow problem of the full compressible Navier–Stokes–Korteweg equations.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553694","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":"Some fixed point results on interpolative metric spaces","authors":"Erdal Karapınar ,&nbsp;Ravi P. Agarwal","doi":"10.1016/j.nonrwa.2024.104244","DOIUrl":"10.1016/j.nonrwa.2024.104244","url":null,"abstract":"<div><div>This paper aims to introduce some basic fixed point theorems on interpolative metric space that is a natural extension of standard metric space.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535933","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":"Approximation theorem of quaternion-valued almost periodic functions of two variables","authors":"Chao Wang ,&nbsp;Ling Guo ,&nbsp;Ravi P. Agarwal","doi":"10.1016/j.nonrwa.2024.104245","DOIUrl":"10.1016/j.nonrwa.2024.104245","url":null,"abstract":"<div><div>In this paper, the quaternion Fourier-Stieltjes transform of two variables is studied. By orthogonal-split method, some fundamental properties of the quaternion-valued almost periodic functions of two variables are obtained. Through introducing the almost periodic approximation via quaternion Fourier-Stieltjes integrals, we establish the quaternion orthogonal-split mean-value theorem. Finally, the approximation theorem of quaternion-valued almost periodic functions of two variables is established.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535932","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":"Local in time solution to an integro-differential system for motion with large deformations and defects","authors":"Abramo Agosti ,&nbsp;Michel Frémond","doi":"10.1016/j.nonrwa.2024.104231","DOIUrl":"10.1016/j.nonrwa.2024.104231","url":null,"abstract":"<div><div>In this paper we consider and generalize a model, recently proposed and analytically investigated in its quasi-stationary approximation by the authors and a co-author, for the motion of a medium with large deformations and conditional compatibility, with occurrence of defects when the magnitude of an internal force is above a given threshold. The model takes the form of a system of integro-differential coupled equations, expressed in terms of the stretch and the rotation tensors variables. Here, its derivation is generalized to consider mixed boundary conditions, which may represent a wider range of physical applications then the case with Dirichlet boundary conditions considered in our previous contribution. This also introduces nontrivial technical difficulties in the theoretical framework, related to the definition and the regularity of the solutions of elliptic operators with mixed boundary conditions. As a novel contribution, we develop the analysis of the fully non-stationary version of the system where we consider inertia. In this context, we prove the existence of a local in time weak solution in three space dimensions, employing techniques from PDEs and convex analysis.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535939","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}