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Indexed by:期刊论文

Date of Publication:2012-12-15

Journal:JOURNAL OF DIFFERENTIAL EQUATIONS

Included Journals:SCIE、Scopus

Volume:253

Issue:12

Page Number:3286-3303

ISSN No.:0022-0396

Key Words:Pseudo-parabolic equation; Second critical exponent; Life span

Abstract:This paper studies the second critical exponent and life span of solutions for the pseudo-parabolic equation u(t) - k Delta u(t) = Delta u + u(p) in R-n x (0, T), with p > 1, k > 0. It is proved that the second critical exponent, i.e., the decay order of the initial data required by global solutions in the coexistence region of global and non-global solutions, is independent of the pseudo-parabolic parameter k. Nevertheless, it is revealed that the viscous term k Delta u(t) relaxes restrictions on the amplitude of the initial data required by the global solutions. Moreover, it is observed that the life span of the non-global solutions will be delayed by the third order viscous term. Finally, some numerical examples are given to illustrate all these results. (C) 2012 Elsevier Inc. All rights reserved.