The profile near blowup time for solutions of diffusion systems coupled with localized nonlinear reactions
type: Item
instance of: scholarly article
title: The profile near blowup time for solutions of diffusion systems coupled with localized nonlinear reactions
zbMATH Open document ID: 1004.35059
DOI: 10.1016/S0362-546X(01)00798-2
author: R. Smith
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-08-25T00:00:00Z
review text: Let \(\Omega\) be a smoothly bounded domain in \(\mathbb{R}^N\), \(x_0\in\Omega\) and \(\lambda_1,\lambda_2>0\). The authors establish the blow-up rate for positive solutions of the system \(u_t=\Delta u+\lambda_1e^{v(x_0,t)}\), \(v_t=\Delta v+\lambda_2e^{u(x_0,t)}\), \((x,t)\in\Omega\times(0,T)\), complemented by the homogeneous Dirichlet boundary conditions on \(\partial\Omega\times(0,T)\). They also show that the blow-up is global and they study the asymptotic behavior of solutions near the boundary \(\partial\Omega\).
reviewed by: Pavol Quittner
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 1788053
zbMATH Keywords: semilinear parabolic system
zbMATH Keywords: localized source
zbMATH Keywords: blow-up rate
zbMATH Keywords: boundary layer
zbMATH Keywords: homogeneous Dirichlet boundary conditions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1788053