Quenching Time for a Semilinear Heat Equation with a Nonlinear Neumann Boundary Condition

Ruifei Li; Liping Zhu; Zhengce Zhang

doi:10.4208/jpde.v27.n3.3

Authors

Ruifei Li School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
Liping Zhu College of Science, Xi’an University of Architecture & Technology, Xi’an 710055, China
Zhengce Zhang School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China

DOI:

https://doi.org/10.4208/jpde.v27.n3.3

Keywords:

Nonlinear Neumann boundary;quenching;quenching time

Abstract

" In this paper we consider the finite time quenching behavior of solutions to a semilinear heat equation with a nonlinear Neumann boundary condition. Firstly, we establish conditions on nonlinear source and boundary to guarantee that the solution doesn't quench for all time. Secondly, we give sufficient conditions on data such that the solution quenches in finite time, and derive an upper bound of quenching time. Thirdly, undermore restrictive conditions, we obtain a lower bound of quenching time. Finally, we give the exact bounds of quenching time of a special example."