{"title":"Global boundedness for an indirect consumption chemotaxis model with signal-dependent motility","authors":"Chun Wu","doi":"10.1016/j.jmaa.2025.129690","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we consider the following chemotaxis system with signal-dependent motility and indirect signal consumption<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mrow><mo>(</mo><mi>D</mi><mo>(</mo><mi>u</mi><mo>)</mo><mi>ϕ</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>)</mo></mrow><mo>,</mo></mtd><mtd><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><mi>Ω</mi><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>−</mo><mi>v</mi><mi>w</mi><mo>,</mo></mtd><mtd><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><mi>Ω</mi><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>w</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>w</mi><mo>−</mo><mi>w</mi><mo>+</mo><mi>u</mi><mo>,</mo></mtd><mtd><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><mi>Ω</mi><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> under the smooth bounded domain <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mspace></mspace><mspace></mspace><mo>(</mo><mi>n</mi><mo>≤</mo><mn>3</mn><mo>)</mo></math></span> with homogeneous Neumann boundary conditions, where the nonlinearities <span><math><mi>D</mi><mo>(</mo><mi>u</mi><mo>)</mo></math></span> and the motility function <em>ϕ</em> satisfy the following condition<span><span><span><math><mi>D</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>=</mo><msup><mrow><mo>(</mo><mi>u</mi><mo>+</mo><mi>a</mi><mo>)</mo></mrow><mrow><mi>m</mi></mrow></msup><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mtext>and</mtext><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mi>ϕ</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>)</mo><mspace></mspace><mspace></mspace><mtext>is positive on</mtext><mspace></mspace><mspace></mspace><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>.</mo></math></span></span></span> It has been demonstrated that, for any sufficiently regular initial data, the associated initial-boundary value problem allows for global classical solutions. Moreover, the asymptotic behavior of the solutions is analyzed and studied.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129690"},"PeriodicalIF":1.2000,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X25004718","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we consider the following chemotaxis system with signal-dependent motility and indirect signal consumption under the smooth bounded domain with homogeneous Neumann boundary conditions, where the nonlinearities and the motility function ϕ satisfy the following condition It has been demonstrated that, for any sufficiently regular initial data, the associated initial-boundary value problem allows for global classical solutions. Moreover, the asymptotic behavior of the solutions is analyzed and studied.
期刊介绍:
The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
Papers are sought which employ one or more of the following areas of classical analysis:
• Analytic number theory
• Functional analysis and operator theory
• Real and harmonic analysis
• Complex analysis
• Numerical analysis
• Applied mathematics
• Partial differential equations
• Dynamical systems
• Control and Optimization
• Probability
• Mathematical biology
• Combinatorics
• Mathematical physics.