Global existence and finite time blowup for a nonlocal semilinear pseudo-parabolic equation

Advances in Nonlinear Analysis

article

Xingchang Wang¹  Runzhang Xu¹ 

[1] College of Automation, Harbin Engineering University;College of Mathematical Sciences, Harbin Engineering University

关键词: Semilinear parabolic equation;    nonlocal source;    potential well;   

DOI  :  10.1515/anona-2020-0141

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

In this paper, the initial boundary value problem for a nonlocal semilinear pseudo-parabolic equation is investigated, which was introduced to model phenomena in population dynamics and biological sciences where the total mass of a chemical or an organism is conserved. The existence, uniqueness and asymptotic behavior of the global solution and the blowup phenomena of solution with subcritical initial energy are established. Then these results are extended parallelly to the critical initial energy. Further the blowup phenomena of solution with supercritical initial energy is proved, but the existence, uniqueness and asymptotic behavior of the global solution with supercritical initial energy are still open.

【 授权许可】

CC BY