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

Title:

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

Creator:

Fujie, Kentarou and Yokota, Tomomi

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a53361e1-6a0e-43cd-9b32-585deed4b7cb
uuid:a53361e1-6a0e-43cd-9b32-585deed4b7cb
doi:10.21136/MB.2014.144140

Subject:

chemotaxis, global existence, and boundedness

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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 0 < χ(v) ≤ χ0/vk (k ≥ 1, χ0 > 0) and λ1 − µ1u ≤ f(u) ≤ λ2 − µ2u (λ1, λ2, µ1, µ2 > 0). It is shown that if χ0 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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

639-647

Source:

Mathematica bohemica | 2014 Volume:139 | Number:4

Harvested from:

CDK

Metadata only:

false