Non-simultaneous blow-up for \(n\)-componential parabolic systems
type: Item
instance of: scholarly article
title: Non-simultaneous blow-up for \(n\)-componential parabolic systems
zbMATH Open document ID: 1197.35063
author: Bingchen Liu
author: Fengjie Li
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-07-24T00:00:00Z
review text: The authors consider the system of semilinear parabolic equations \((u_i)_t=\Delta u_i+u_i^{p_i}\), \(i=1,2,\dots,n\), in a domain \(\Omega\subset\mathbb R^N\), coupled via the nonlinear boundary conditions \(\partial u_i/\partial\eta=u_{i+1}^{q_{i+1}}\), \(i=1,2,\dots n\). They first find necessary and sufficient conditions on the exponents guaranteeing blow-up of all positive solutions. Then, considering the blow-up case for \(\Omega=\{x:|x|<R\}\) and restricting themselves to radial positive solutions increasing both in \(|x|\) and \(t\), they find necessary and sufficient conditions for simultaneous and non-simultaneous blow-up. They also obtain blow-up rate estimates.
reviewed by: Pavol Quittner
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35K51
Mathematics Subject Classification ID: 35K58
Mathematics Subject Classification ID: 35K61
zbMATH DE Number: 5586883
zbMATH Keywords: blow-up
zbMATH Keywords: blow-up rate
zbMATH Keywords: nonlinear boundary conditions
MaRDI profile type: Publication
full work available at URL: j.na.2009.02.019
OpenAlex ID: W2039245111
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DOI: 10.1016/J.NA.2009.02.019
description: scientific article; zbMATH DE number 5586883