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Indexed by:期刊论文

Date of Publication:2008-11-01

Journal:COMPUTERS & MATHEMATICS WITH APPLICATIONS

Included Journals:SCIE、EI、Scopus

Volume:56

Issue:9

Page Number:2294-2304

ISSN No.:0898-1221

Key Words:Nonlinear diffusion; Localized source; Blow-up rate; Blow-up profile; Blow-up set; Total blow-up; Single point blow-up

Abstract:In this paper we study a localized nonlinear diffusion equation u(t) = Delta u(m) + lambda(1)u(p) + lambda(2)u(q)(0, t) subject to null Dirichlet boundary condition with p, q >= 0, max{p, q) > m > 1, and lambda(1), lambda(2) > 0. We investigate interactions among the localized and local sources, nonlinear diffusion with the zero boundary value condition to establish blow-up rates and uniform blow-up profiles of solutions under different dominations. In addition, as results of the interactions of multiple nonlinearities, the blow-up sets of solutions, namely, total versus single point blow-up of solutions are also determined. (C) 2008 Elsevier Ltd. All rights reserved.