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Indexed by:期刊论文

Date of Publication:2008-10-01

Journal:NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Included Journals:SCIE、EI、Scopus

Volume:69

Issue:7

Page Number:2274-2285

ISSN No.:0362-546X

Key Words:quenching; non-simultaneous quenching; quenching set; quenching rate; nonlinear parabolic system; dirichlet boundary condition

Abstract:This paper deals with finite-time quenching for the nonlinear parabolic system with coupled singular absorptions: u(1) = Delta u - v(-p), v(t) = Delta v-u(-q) in Omega x (0, T) subject to positive Dirichlet boundary conditions, where p, q > 0, Omega is a bounded domain in R-N with smooth boundary. We obtain the sufficient conditions for global existence and finite-time quenching of solutions, and then deter-mine the blow-up of time-derivatives and the quenching set for the quenching solutions. As the main results of the paper, a very clear picture is obtained for radial solutions with Omega = B-R: the quenching is simultaneous if p, q >= 1, and non-simultaneous if p < 1 <= q or q < 1 <= p; if p, q < 1 with R > root 2N, then both simultaneous and non-simultaneous quenching may happen, depending on the initial data. In determining the non-simultaneous quenching criteria of the paper, some new ideas have been introduced to deal with the coupled singular inner absorptions and inhomogeneous Dirichlet boundary value conditions, in addition to techniques frequently used in the literature. (C) 2007 Elsevier Ltd. All rights reserved.