Global existence and finite time blow-up of the solution for a thin-film equation with high initial energy

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:458

Article

Xu, Guangyu¹  Zhou, Jun^1,2 

[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

[2] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China

关键词: Thin-film equation;    Global existence;    Blow-up;    High initial energy;   

DOI  :  10.1016/j.jmaa.2017.09.031

来源: Elsevier

【 摘 要 】

This paper is devoted to the study of a thin-film equation, which was considered extensively in recent years. We obtain the conditions for global existence and finite time blow-up of solution for the high initial energy case, i.e., J(u(0)) > d, while the previous works only considered the case J(uo) <= d, here d is the mountain pass level. Moreover, for the blow-up solution with J(uo) <= d, we obtain the lower bound estimate of the blow-up time and blow-up rate. (C) 2017 Published by Elsevier Inc.

【 授权许可】

Free