Global attractivity for reaction-diffusion systems. The case of nondiagonal diffusion matrices
type: Item
instance of: scholarly article
title: Global attractivity for reaction-diffusion systems. The case of nondiagonal diffusion matrices
zbMATH Open document ID: 0794.35077
published in: Journal of Mathematical Analysis and Applications
publication date: 1994-08-31T00:00:00Z
review text: The authors consider reaction-diffusion systems with cross diffusion of the form \[ \partial_ t{\mathbf u}=D\Delta{\mathbf u}+f(u) \] subject to the boundary condition \(\beta D\partial_ \nu{\mathbf u}=\alpha({\mathbf u}^*-{\mathbf u})\), where \({\mathbf u}^*\) is a given vector in \(\mathbb{R}^ m\), \(\alpha\) and \(\beta\) are nonnegative constants with \(\alpha+\beta>0\) and \(D\) is a positive definite matrix on \(\mathbb{R}^ m\). They study the convergence to a uniform steady state assuming that such a steady state exists for the associated kinetic system. The main tool is LaSalle's invariance principle.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 480458
zbMATH Keywords: reaction-diffusion systems with cross diffusion
zbMATH Keywords: LaSalle's invariance principle
author: Vincenzo Capasso
author: A. Di Liddo
reviewed by: Georg Hetzer
MaRDI profile type: Publication
full work available at URL: jmaa.1993.1274
OpenAlex ID: W1974251315
DOI: 10.1006/JMAA.1993.1274
description: scientific article; zbMATH DE number 480458