Semilinear parabolic systems modelling spatially inhomogeneous exothermic reactions
type: Item
instance of: scholarly article
title: Semilinear parabolic systems modelling spatially inhomogeneous exothermic reactions
zbMATH Open document ID: 0790.35047
author: C. B. Martin
author: W. E. Fitzgibbon
published in: Journal of Mathematical Analysis and Applications
publication date: 1994-05-18T00:00:00Z
review text: The authors consider reaction-diffusion systems of the form: \[ \partial_ t u-d_ 1\Delta =-uvF(\theta),\qquad \partial_ t v-d_ 2\Delta =uvf(\theta)- \mu g(v),\qquad \partial_ t \theta-d_ 3\Delta =\mu g(v) \] on a smooth bounded domain of \(\mathbb{R}^ n\) subject to homogeneous Neumann boundary conditions. The function \(f\) is given by \(f(\theta)=0\), if \(\theta\leq 0\), and \(f(\theta)= Ke^{-E/\theta}\), \(K,E\in (0,\infty)\), if \(\theta>0\), and \(g(v)\) is either equal to \(v\) or to \(v^ 2\). The authors establish the existence and uniqueness of global nonnegative solutions for nonnegative initial conditions and show uniform convergence of such solutions to spatially homogeneous steady states as \(t\to\infty\).
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 484009
zbMATH Keywords: reaction-diffusion systems
zbMATH Keywords: homogeneous Neumann boundary conditions
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: global nonnegative solutions
zbMATH Keywords: nonnegative initial conditions
zbMATH Keywords: spatially homogeneous steady states
reviewed by: Georg Hetzer
MaRDI profile type: Publication
full work available at URL: jmaa.1993.1299
OpenAlex ID: W2063490092
DOI: 10.1006/JMAA.1993.1299
description: scientific article; zbMATH DE number 484009