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

Ruifei Li , Liping Zhu & Zhengce Zhang

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

Published online: 2014-09

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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.

  • Keywords

Nonlinear Neumann boundary quenching quenching time

  • AMS Subject Headings

35A01 35B40 35K05 35K55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-27-217, author = {}, title = {Quenching Time for a Semilinear Heat Equation with a Nonlinear Neumann Boundary Condition}, journal = {Journal of Partial Differential Equations}, year = {2014}, volume = {27}, number = {3}, pages = {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.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v27.n3.3}, url = {http://global-sci.org/intro/article_detail/jpde/5138.html} }
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