Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2011-04-01

Journal: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Included Journals: EI、SCIE、Scopus

Volume: 74

Issue: 7

Page Number: 2508-2514

ISSN: 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.