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Indexed by:期刊论文

Date of Publication:2013-01-01

Journal:APPLIED MATHEMATICS AND COMPUTATION

Included Journals:SCIE、EI、Scopus

Volume:219

Issue:9

Page Number:4219-4224

ISSN No.:0096-3003

Key Words:Reaction-diffusion system; Localized source; Mixed-type coupling; Blow-up profile; Critical Fujita exponent

Abstract:This paper deals with asymptotic behavior of solutions to a reaction-diffusion system coupled via localized and local sources: u(t) = Delta u + nu(p)(x*(t), t), nu(t) = Delta nu + u(q). Both the initial-boundary problem with null Dirichlet boundary condition and the Cauchy problem are considered to study the interaction between the two kinds of sources. For the initial-boundary problem we prove that the nonglobal solutions blow up everywhere in the bounded domain with uniform blow-up profiles. In addition, it is interesting to observe that the Cauchy problem admits an infinity Fujita exponent, namely, the solutions blow up under any nontrivial and nonnegative initial data whenever pq > 1. All these imply that the blow-up behavior of solutions is governed by the localized source for the two problems with mixed-type coupling. (C) 2012 Elsevier Inc. All rights reserved.