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Indexed by:期刊论文

Date of Publication:2013-02-15

Journal:JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Included Journals:SCIE、Scopus

Volume:398

Issue:2

Page Number:879-885

ISSN No.:0022-247X

Key Words:Critical Fujita exponent; Fast diffusion; Potential; Global solutions; Blow-up

Abstract:This paper studies the Cauchy problem for positive solutions of the fast diffusion equation with source and quadratically decaying potential u(t) = Delta u(m) - V(x)u(m) + u(P) in R-n x (0, T), where 1 - 2/m alpha+n < m < 1, p > 1, n >= 2, V(x) similar to omega/vertical bar x vertical bar(2) with omega >= 0 as vertical bar x vertical bar -> infinity, and alpha is the positive root of m alpha (m alpha + n - 2) - w = 0. We obtain the critical Fujita exponent Pc = m to the problem in the sense that every nontrivial solution blows up in finite time when 1 < p <= pc, and there are both global and non-global solutions if p > pc. (C) 2012 Elsevier Inc. All rights reserved.