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Indexed by:期刊论文

Date of Publication:2011-04-01

Journal:NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Included Journals:Scopus、SCIE、EI

Volume:74

Issue:7

Page Number:2508-2514

ISSN No.:0362-546X

Key Words:Fast diffusion; Localized reaction; Blow-up; Global existence; Fujita exponent; Blow-up rate; Blow-up set

Abstract:This paper studies the Cauchy problem for the fast diffusion equation with a localized reaction. We establish the Fujita type theorem to the problem, and then obtain the diffusion-independent blow-up rate for the non-global solutions. Moreover, we prove that the blow-up set for the problem consists of a single point under large initial data. These conclusions are quite different from those for the slow diffusion case. (C) 2010 Elsevier Ltd. All rights reserved.