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Indexed by:期刊论文

Date of Publication:2012-12-01

Journal:MATHEMATICAL AND COMPUTER MODELLING

Included Journals:Scopus、SCIE、EI

Volume:56

Issue:11-12

Page Number:247-256

ISSN No.:0895-7177

Key Words:Evolution p-Laplacian equation; Weighted source; Global existence; Blow-up; Second critical exponent; Life span

Abstract:This paper studies the Cauchy problem for the evolution p-Laplacian equation with weighted source: u(t) = div(|del u|(p-2)del u)+|x|(m)u(q) in R-n x (0, T), where 2n/(n + 1) < p < 2, m > n(2 - p) - p, q > 1. We obtain the second critical exponent on decay orders of initial data at infinity to identify global and non-global solutions in the coexistence region of the two kinds of solutions. In addition, we determine the life span of the non-global solutions in the case of m = 0. (C) 2011 Elsevier Ltd. All rights reserved.