Global and blow-up solutions for a nonlinear reaction diffusion equation with Robin boundary conditions

Boundary Value Problems

Huimin Tian¹  Lingling Zhang¹ 

[1]Department of Mathematics, Taiyuan University of Technology

关键词: Reaction diffusion equations;    Blow-up;    Global;    Lower and upper bounds;   

DOI  :  10.1186/s13661-020-01363-y

来源: DOAJ

【 摘 要 】

Abstract In the paper, we investigate global and blow-up solutions for a class of nonlinear reaction diffusion equations with Robin boundary conditions. By using auxiliary functions and a first-order differential inequality technique, we establish conditions on the data to prove the existence of global solution. Moreover, based on maximum principles, we obtain a criterion that guarantees the occurrence of the blow-up. When blow-up occurs, we discuss an upper bound and a lower bound on blow-up time. At last, we apply two examples to illustrate our main results.

【 授权许可】

Unknown