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Title: Boundedness of solutions to parabolic-elliptic chemotaxis-growth systems with signal-dependent sensitivity (English)
Author: Fujie, Kentarou
Author: Yokota, Tomomi
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
Volume: 139
Issue: 4
Year: 2014
Pages: 639-647
Summary lang: English
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Category: math
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Summary: This paper deals with parabolic-elliptic chemotaxis systems with the sensitivity function $\chi (v)$ and the growth term $f(u)$ under homogeneous Neumann boundary conditions in a smooth bounded domain. Here it is assumed that $0< \chi (v)\leq {{\chi }_0}/{v^k}$ $(k\geq 1$, ${\chi }_0>0)$ and $\lambda _1-\mu _1 u \leq f(u)\leq \lambda _2-\mu _2 u$ $(\lambda _1,\lambda _2,\mu _1,\mu _2>0)$. It is shown that if $\chi _0$ is sufficiently small, then the system has a unique global-in-time classical solution that is uniformly bounded. This boundedness result is a generalization of a recent result by K. Fujie, M. Winkler, T. Yokota. (English)
Keyword: chemotaxis
Keyword: global existence
Keyword: boundedness
MSC: 35A01
MSC: 35B40
MSC: 35B45
MSC: 35K60
MSC: 35M33
MSC: 92C17
idZBL: Zbl 06433687
idMR: MR3306853
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Date available: 2015-02-04T09:21:56Z
Last updated: 2016-01-04
Stable URL: http://hdl.handle.net/10338.dmlcz/144140
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