Blow-Up Solutions and Global Existence for a Kind of Quasilinear Reaction-Diffusion Equations
Lingling Zhang
Taiyuan University of Technology, ChinaNa Zhang
Taiyuan University of Technology, Taiyuan, Shanxi, ChinaLixiang Li
Taiyuan University of Technology, Taiyuan, Shanxi, China
![Blow-Up Solutions and Global Existence for a Kind of Quasilinear Reaction-Diffusion Equations cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-zaa-volume-33-issue-3.png&w=3840&q=90)
Abstract
In this paper, we study the blow-up solutions and global existence for a quasilinear reaction-diffusion equation including a gradient term and nonlinear boundary condition:
where is a bounded domain with smooth boundary . The sufficient conditions are obtained for the existence of a global solution and a blow-up solution. 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 specified under some appropriate assumptions for the nonlinear system functions , and initial value by constructing suitable auxiliary functions and using maximum principles.
Cite this article
Lingling Zhang, Na Zhang, Lixiang Li, Blow-Up Solutions and Global Existence for a Kind of Quasilinear Reaction-Diffusion Equations. Z. Anal. Anwend. 33 (2014), no. 3, pp. 247–258
DOI 10.4171/ZAA/1509