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

Quenching Time for a Semilinear Heat Equation with a Nonlinear Neumann Boundary Condition
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Year:    2014

Author:    Ruifei Li, Liping Zhu, Zhengce Zhang

Journal of Partial Differential Equations, Vol. 27 (2014), Iss. 3 : pp. 217–228

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

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

Journal of Partial Differential Equations, Vol. 27 (2014), Iss. 3 : pp. 217–228

Published online:    2014-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    Nonlinear Neumann boundary

Author Details

Ruifei Li

Liping Zhu

Zhengce Zhang

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