Self-similar solutions to a parabolic system modeling chemotaxis
type: Item
instance of: scholarly article
title: Self-similar solutions to a parabolic system modeling chemotaxis
zbMATH Open document ID: 1016.35037
author: Yūki Naito
author: Takashi Suzuki
author: Kiyoshi Yoshida
published in: Journal of Differential Equations
publication date: 2002-10-16T00:00:00Z
review text: This paper concerns the forward self-similar solutions to a parabolic system modeling chemotaxis \[ u_t= \nabla\cdot(\nabla u- u\nabla v),\quad \tau v_t=\Delta v+u \] in \(\mathbb{R}^2\), where \(\tau> 0\) is a constant. By a Liouville-type result and using the method of moving planes it is proved that self-similar solutions \((u,v)\) must be radially symmetric about the origin. The structure of the set of self-similar solution has been investigated.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 92C17
zbMATH DE Number: 1815486
zbMATH Keywords: radial symmetry
zbMATH Keywords: blow-up
zbMATH Keywords: method of moving planes
reviewed by: Sebastian Aniţa
MaRDI profile type: Publication
full work available at URL: jdeq.2001.4146
OpenAlex ID: W1996447953
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DOI: 10.1006/JDEQ.2001.4146
description: scientific article; zbMATH DE number 1815486