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Indexed by:期刊论文

Date of Publication:2010-06-01

Journal:NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS

Included Journals:SCIE、EI、Scopus

Volume:11

Issue:3

Page Number:2136-2140

ISSN No.:1468-1218

Key Words:Fujita exponents; Nonlinear diffusion; Blow-up; Localized source

Abstract:This paper deals with Cauchy problem to nonlinear diffusion u(t) = Delta u(m) + lambda 1u(p1) (x, t) + lambda(2)u(p2)(x*(t), t) with m >= 1, p(1), lambda(1) >= 0 (i = 1, 2) and x*(t) Holder continuous. A new phenomenon is observed that the critical Fujita exponent p(c) = + infinity whenever lambda(2) > 0. More precisely, the solution blows up under any nontrivial and nonnegative initial data for all p = max{P(1) , P(2)} is an element of (1, +infinity). This result is then extended to a coupled system with localized sources as well as the cases with other nonlineanties. (C) 2009 Elsevier Ltd. All rights reserved.