Unlimited growth in logarithmic Keller-Segel systems
type: Item
instance of: scholarly article
title: Unlimited growth in logarithmic Keller-Segel systems
zbMATH Open document ID: 1480.35383
author: Michael Winkler
published in: Journal of Differential Equations
publication date: 2021-12-22T00:00:00Z
review text: A parabolic system describing chemotaxis with logarithmic sensitivity function is considered in balls of \(\mathbb R^n\) \[\varepsilon u_t=\Delta u-\chi\nabla\cdot(\frac{u}{v}\nabla v),\] \[v_t=\Delta v-v+u.\] The singular limit \(\varepsilon\searrow 0\) is studied, and the phenomenon of unboundedness of some radially symmetric solutions is shown for small \(\varepsilon>0\), under the assumption \(\chi>\frac{n}{n-2}\). Thus, the property of unboundedness of \(u\) known for \(\varepsilon=0\) is shared by a parabolically perturbed problem in the same range of the parameter \(\chi\).
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35K59
Mathematics Subject Classification ID: 92C17
zbMATH DE Number: 7450432
zbMATH Keywords: chemotaxis
zbMATH Keywords: logarithmic sensitivity
zbMATH Keywords: unbounded solution
zbMATH Keywords: singular limit
MaRDI profile type: Publication
full work available at URL: j.jde.2021.11.026
OpenAlex ID: W3217323004
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DOI: 10.1016/J.JDE.2021.11.026
description: scientific article; zbMATH DE number 7450432