Well-posedness for chemotaxis dynamics with nonlinear cell diffusion
type: Item
instance of: scholarly article
title: Well-posedness for chemotaxis dynamics with nonlinear cell diffusion
zbMATH Open document ID: 1272.35120
published in: Journal of Mathematical Analysis and Applications
publication date: 2013-04-22T00:00:00Z
review text: This article is concerned with the well-posedness of reaction-diffusion chemotaxis systems with a nonlinear diffusion coefficient, depending on the cell density, and a stationary chemo-attractant. Two cases of diffusion coefficients are discussed: the first case assumes a smooth, locally bounded diffusion coefficient. The second case assumes a singularity in the diffusion coefficient for a finite value of the cell density. Conditions for both local and global existence of weak solutions are investigated. Results include small and large data global existence results and, under more restrictive conditions, uniqueness results on all or part of the interval of existence.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 92C17
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35K40
zbMATH DE Number: 6156135
zbMATH Keywords: \(m\)-accretive operators
zbMATH Keywords: global weak solutions
zbMATH Keywords: well-posedness
author: Gabriela Marinoschi
MaRDI profile type: Publication
full work available at URL: j.jmaa.2013.01.031
OpenAlex ID: W1967220598
Wikidata QID: Q60581987
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DOI: 10.1016/J.JMAA.2013.01.031
description: scientific article; zbMATH DE number 6156135