Global existence and finite time blow up for a degenerate reaction-diffusion system
type: Item
instance of: scholarly article
title: Global existence and finite time blow up for a degenerate reaction-diffusion system
zbMATH Open document ID: 1063.35093
author: Weibing Deng
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2005-02-22T00:00:00Z
review text: The paper deals with the blow up and global existence of the nonnegative solutions to the degenerate parabolic system \[ u_t = \Delta u^m + u^{\alpha} v^p, \qquad v_t = \Delta v^n + u^q v^{\beta}, \qquad (x,t) \in \Omega \times (0,T) \] with homogeneous Dirichlet boundary data and nonnegative bounded initial functions. Here \(\Omega \subset \mathbb{R}^N\) is a bounded domain with smooth boundary and \(m,n > 1\), \( \alpha, \beta \geq 0\), \(p,q >0\). The system above describes processes of heat diffusion and combustion in two-component continua. Its special form \[ u_t = \Delta u^{\nu + 1} + v^p, \qquad \quad v_t = \Delta u^{\mu+1} + u^q \] was investigated by many authors (detailed quotations are given). The purpose of the paper under review is to extend these results.
reviewed by: Hanna Marcinkowska
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 80A25
zbMATH DE Number: 2136698
zbMATH Keywords: homogeneous Dirichlet boundary data
zbMATH Keywords: nonnegative bounded initial functions
zbMATH Keywords: combustion in two-component continua
MaRDI profile type: Publication
full work available at URL: j.na.2004.10.016
OpenAlex ID: W2069220038
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DOI: 10.1016/J.NA.2004.10.016
description: scientific article; zbMATH DE number 2136698