A blow-up result for a quasilinear chemotaxis system with logistic source in higher dimensions
type: Item
instance of: scholarly article
title: A blow-up result for a quasilinear chemotaxis system with logistic source in higher dimensions
zbMATH Open document ID: 1391.35377
author: Ke Lin
author: Hua Zhong
author: Chunlai Mu
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-05-09T00:00:00Z
review text: A quasilinear parabolic-elliptic system of chemotaxis \(u_t=\nabla\cdot(D(u)\nabla u-\chi u\nabla v) +f(u)\), \(\Delta v -\frac{1}{|\Omega|}\int_\Omega u(x,t)dx+u=0\) is studied with a power-like diffusion coefficient \(D(u)\geq D_0u^m\), and a logistic type source \(f(u)=au-bu^\kappa\) in a bounded domain \(\Omega\subset \mathbb R^n\). The authors prove a global in time existence result under some assumptions on \(m\), \(\kappa\), \(n\). Moreover, when \(n\geq 5\), \(m\in[0,\frac{4}{n}-1)\), and \(\kappa\in\left(1,\frac{(3+m)n-2}{2n-2}\right)\), there exist radially symmetric initial data in the ball of arbitrarily prescribed mass such that the corresponding solutions blow up in a finite time. This is an extension of result of \textit{M. Winkler} in [J. Math. Anal. Appl. 384, No. 2, 261--272 (2011; Zbl 1241.35028)] to the quasilinear case, and gives a correction to the arguments in [\textit{P. Zheng} et al., Discrete Contin. Dyn. Syst. 35, No. 5, 2299--2323 (2015; Zbl 1307.35067)].
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 35B44
zbMATH DE Number: 6867356
zbMATH Keywords: quasilinear chemotaxis
zbMATH Keywords: logistic source
zbMATH Keywords: blowup
MaRDI profile type: Publication
full work available at URL: j.jmaa.2018.04.015
OpenAlex ID: W2796764078
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Wikidata QID: Q130038207
DOI: 10.1016/J.JMAA.2018.04.015
description: scientific article; zbMATH DE number 6867356