Boundedness of solutions to parabolic-elliptic chemotaxis-growth systems with signal-dependent sensitivity

Kentarou Fujie; Tomomi Yokota

Boundedness of solutions to parabolic-elliptic chemotaxis-growth systems with signal-dependent sensitivity

Kentarou Fujie, Tomomi Yokota

SCI - Mathematics

Tokyo University of Science

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

This paper deals with parabolic-elliptic chemotaxis systems with the sensitivity function χ(v) and the growth term f(u) under homogeneous Neumann boundary conditions in a smooth bounded domain. Here it is assumed that (Formula presented.) and (Formula presented.). It is shown that if χ0 is sufficiently small, then the system has a unique global-in-time classical solution that is uni- formly bounded. This boundedness result is a generalization of a recent result by K.Fujie, M.Winkler, T.Yokota.

Original language	English
Pages (from-to)	639-647
Number of pages	9
Journal	Mathematica Bohemica
Volume	139
Issue number	4
Publication status	Published - 2014

Keywords

Boundedness
Chemotaxis
Global existence

Cite this

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abstract = "This paper deals with parabolic-elliptic chemotaxis systems with the sensitivity function χ(v) and the growth term f(u) under homogeneous Neumann boundary conditions in a smooth bounded domain. Here it is assumed that (Formula presented.) and (Formula presented.). It is shown that if χ0 is sufficiently small, then the system has a unique global-in-time classical solution that is uni- formly bounded. This boundedness result is a generalization of a recent result by K.Fujie, M.Winkler, T.Yokota.",

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T1 - Boundedness of solutions to parabolic-elliptic chemotaxis-growth systems with signal-dependent sensitivity

AU - Fujie, Kentarou

AU - Yokota, Tomomi

PY - 2014

Y1 - 2014

N2 - This paper deals with parabolic-elliptic chemotaxis systems with the sensitivity function χ(v) and the growth term f(u) under homogeneous Neumann boundary conditions in a smooth bounded domain. Here it is assumed that (Formula presented.) and (Formula presented.). It is shown that if χ0 is sufficiently small, then the system has a unique global-in-time classical solution that is uni- formly bounded. This boundedness result is a generalization of a recent result by K.Fujie, M.Winkler, T.Yokota.

AB - This paper deals with parabolic-elliptic chemotaxis systems with the sensitivity function χ(v) and the growth term f(u) under homogeneous Neumann boundary conditions in a smooth bounded domain. Here it is assumed that (Formula presented.) and (Formula presented.). It is shown that if χ0 is sufficiently small, then the system has a unique global-in-time classical solution that is uni- formly bounded. This boundedness result is a generalization of a recent result by K.Fujie, M.Winkler, T.Yokota.

KW - Boundedness

KW - Chemotaxis

KW - Global existence

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JO - Mathematica Bohemica

JF - Mathematica Bohemica

IS - 4

ER -

Boundedness of solutions to parabolic-elliptic chemotaxis-growth systems with signal-dependent sensitivity

Abstract

Keywords

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