Second critical exponent and life span for pseudo-parabolic equation

[摘要] 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.

[发布日期] 2012-12-15

[关键词] Pseudo-parabolic equation;Second critical exponent;Life span