The nonsymmetric case of the Keller-Segel model in chemotaxis: some recent results.
type: Item
instance of: scholarly article
title: The nonsymmetric case of the Keller-Segel model in chemotaxis: some recent results.
zbMATH Open document ID: 1056.35086
DOI: 10.1007/PL00001455
author: Dirk Horstmann
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2001-01-01T00:00:00Z
review text: This paper studies the non-symmetric (e.g. non-radical) case of the Keller-Segel, reaction-diffuson model of chemotaxis. It reviews known global existence and blow-up results. Particular emphasis is placed on ``non-symmetric'' solutions, and it is proved that if a solution blows-up in finite time then blow up takes place at the boundary of a smooth domain. Nontrivial stationary solutions are established using variational methods. The paper complements that of \textit{M. A. Herrero} [Asymptotic properties of reaction-diffusion systems modeling chemotaxis. In: Spigler, Renato (ed.) Applied and industrial mathematics, Venice-2, 1998. Dordrecht, Kluwer, 89--108 (2000; Zbl 1006.35052)].
reviewed by: B. D. Sleeman
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 92B05
Mathematics Subject Classification ID: 92C15
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92C17
zbMATH DE Number: 1722188
zbMATH Keywords: global existence and blow-up results
zbMATH Keywords: blow up takes place at the boundary
MaRDI profile type: Publication
full work available at URL: pl00001455
OpenAlex ID: W2064997248
description: scientific article; zbMATH DE number 1722188