{"title":"Long term spatial homogeneity for a chemotaxis model with local sensing and consumption","authors":"Philippe Laurençot","doi":"10.4310/cms.2023.v21.n6.a14","DOIUrl":null,"url":null,"abstract":"Global weak solutions to a chemotaxis model with local sensing and consumption are shown to converge to spatially homogeneous steady states in the large time limit, when the motility is assumed to be positive and $C^1$-smooth on $[0,\\infty)$. The result is valid in arbitrary space dimension $n \\geq1$ and extends a previous result which only deals with space dimensions $n \\in {\\lbrace 1,2,3 \\rbrace}$.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"1226 ","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cms.2023.v21.n6.a14","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 3
Abstract
Global weak solutions to a chemotaxis model with local sensing and consumption are shown to converge to spatially homogeneous steady states in the large time limit, when the motility is assumed to be positive and $C^1$-smooth on $[0,\infty)$. The result is valid in arbitrary space dimension $n \geq1$ and extends a previous result which only deals with space dimensions $n \in {\lbrace 1,2,3 \rbrace}$.
期刊介绍:
Covers modern applied mathematics in the fields of modeling, applied and stochastic analyses and numerical computations—on problems that arise in physical, biological, engineering, and financial applications. The journal publishes high-quality, original research articles, reviews, and expository papers.