Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2010-06-01

Journal: NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS

Included Journals: Scopus、EI、SCIE

Volume: 11

Issue: 3

Page Number: 2136-2140

ISSN: 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.