Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2013-01-01

Journal: APPLIED MATHEMATICS AND COMPUTATION

Included Journals: Scopus、EI、SCIE

Volume: 219

Issue: 9

Page Number: 4219-4224

ISSN: 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.