Blow-up solutions, global existence, and exponential decay estimates for second order parabolic problems

Boundary value problems

Juntang Ding¹  Ming Wang¹ 

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

关键词: blow-up solution;    global existence;    exponential decay estimate;    35K60;    35K20;   

DOI  :  10.1186/s13661-015-0429-y

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we study the blow-up solutions, global existence, and exponential decay estimates for a class of second order parabolic problems with Dirichlet boundary conditions. By constructing auxiliary functions and using maximum principles, the sufficient conditions for the existence of the blow-up solution, the sufficient conditions for the global existence of the solution, an upper bound for the ‘blow-up time’, and some explicit exponential decay bounds for the solution and its derivatives are specified.

【 授权许可】

CC BY