Volume 27, Issue 3
Quenching Time for a Semilinear Heat Equation with a Nonlinear Neumann Boundary Condition

Ruifei Li ,  Liping Zhu and Zhengce Zhang

10.4208/jpde.v27.n3.3

J. Part. Diff. Eq., 27 (2014), pp. 217-228.

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  • 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.

  • History

Published online: 2014-09

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