Pointwise bounds for linear reaction-diffusion systems and an extension to nonlinear problems
type: Item
instance of: scholarly article
title: Pointwise bounds for linear reaction-diffusion systems and an extension to nonlinear problems
zbMATH Open document ID: 0669.35050
DOI: 10.1016/0022-247X(88)90144-8
author: Michael Plum
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: The author considers systems of the form \[ \partial u^ i/\partial t- div(d_ iA(\nabla u^ i))+C^ i_ ju^ j=r^ i\quad in\quad \Omega \times (0,\infty),\quad i=1,...,n, \] where \(d_ i>0\) are diffusion coefficients, A is a uniformly positive definite symmetric matrix, \(C^ i_ j(x,t)\) and \(r^ i(x,t)\) are continuous functions. \(\Omega\) is a bounded domain in \({\mathbb{R}}^ m\), \(u^ i(x,0)\) is given and the boundary condition is \(Bu^ i=0\) on \(\partial \Omega \times (0,\infty)\) where B is the identity or \(Bu^ i=\nabla u^ iA\nu +bu^ i,\) \(\nu =unit\) outer normal and b a nonnegative scalar function. The main result of the paper is a bound for \(\max | u^ i(x,t)|\) (x\(\in \Omega\), \(i=1,...,n\), \(t\geq 0\}\) in terms of the data.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35K60
zbMATH DE Number: 4096013
zbMATH Keywords: bound
zbMATH Keywords: terms of the data
reviewed by: Robert L. Taylor
MaRDI profile type: Publication
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full work available at URL: 0022-247x(88)90144-8
OpenAlex ID: W2092185343
description: scientific article; zbMATH DE number 4096013