Quasilinear parabolic systems of several components
type: Item
instance of: scholarly article
title: Quasilinear parabolic systems of several components
zbMATH Open document ID: 1032.35079
author: Yuxiang Li
author: Chunhong Xie
published in: Mathematische Annalen
publication date: 2003-12-16T00:00:00Z
review text: The paper deals with blow-up criteria for the homogeneous Cauchy-Dirichlet problem in \(\Omega\times(0,\infty),\) \(\Omega\subset{\mathbb R}^N,\) for the quasilinear parabolic system \[ (u_i)_t=c_i u_i^{\alpha_i} \Biggl(\Delta u_i +\prod_{j=1}^n u_j^{p_{ij}}\Biggr),\quad i=1,2,\ldots,n, \] where \(c_i>0,\) \(\alpha_i>0,\) \(p_{ij}\geq 0,\) \(1\leq i,j\leq n,\) are constants. Set \(I\) for the identity matrix and \(P=(p_{ij})\) which is assumed to be irreducible. The authors show that ``\(I-P\) is singular \(M\)-matrix'' is a critical case in which the first Dirichlet eigenvalue \(\lambda_1\) of the Laplacian in \(\Omega\) plays a fundamental role. This gives various results concerning porous medium systems.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K65
zbMATH DE Number: 2018277
zbMATH Keywords: homogeneous Cauchy-Dirichlet problem
zbMATH Keywords: blow-up
zbMATH Keywords: porous medium systems
MaRDI profile type: Publication
full work available at URL: s00208-003-0459-0
OpenAlex ID: W2039533484
DOI: 10.1007/S00208-003-0459-0
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description: scientific article; zbMATH DE number 2018277