{"title":"Global existence, uniform boundedness, and stabilization in a chemotaxis system with density-suppressed motility and nutrient consumption","authors":"Jie Jiang, P. Laurençot, Yanyan Zhang","doi":"10.1080/03605302.2021.2021422","DOIUrl":null,"url":null,"abstract":"Abstract Well-posedness and uniform-in-time boundedness of classical solutions are investigated for a three-component parabolic system which describes the dynamics of a population of cells interacting with a chemoattractant and a nutrient. The former induces a chemotactic bias in the diffusive motion of the cells and is accounted for by a density-suppressed motility. Well-posedness is first established for generic positive and non-increasing motility functions vanishing at infinity. Growth conditions on the motility function guaranteeing the uniform-in-time boundedness of solutions are next identified. Finally, for sublinearly decaying motility functions, convergence to a spatially homogeneous steady state is shown, with an exponential rate for consumption rates behaving linearly near zero.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2021-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/03605302.2021.2021422","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 12
Abstract
Abstract Well-posedness and uniform-in-time boundedness of classical solutions are investigated for a three-component parabolic system which describes the dynamics of a population of cells interacting with a chemoattractant and a nutrient. The former induces a chemotactic bias in the diffusive motion of the cells and is accounted for by a density-suppressed motility. Well-posedness is first established for generic positive and non-increasing motility functions vanishing at infinity. Growth conditions on the motility function guaranteeing the uniform-in-time boundedness of solutions are next identified. Finally, for sublinearly decaying motility functions, convergence to a spatially homogeneous steady state is shown, with an exponential rate for consumption rates behaving linearly near zero.