Global existence and blow-up for a class of nonlinear reaction diffusion problems

Boundary value problems

Juntang Ding¹ 

[1] School of Mathematical Sciences, Shanxi University, Taiyuan, China

关键词: reaction diffusion problem;    global existence;    blow-up;   

DOI  :  10.1186/s13661-014-0168-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper deals with the global existence and blow-up of the solution for a class of nonlinear reaction diffusion problems. The purpose of this paper is to establish conditions on the data to guarantee the blow-up of the solution at some finite time, and conditions to ensure that the solution remains global. In addition, an upper bound for the ‘blow-up time’, an upper estimate of the ‘blow-up rate’, and an upper estimate of the global solution are also specified. Finally, as applications of the obtained results, some examples are presented. MSC: 35K57, 35K55, 35B05.

【 授权许可】

CC BY