Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2012-12-15

Journal: JOURNAL OF DIFFERENTIAL EQUATIONS

Included Journals: Scopus、SCIE

Volume: 253

Issue: 12

Page Number: 3286-3303

ISSN: 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.