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Volume 27, Issue 3
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

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

  • Email address

liruifei@stu.xjtu.edu.cn (Ruifei Li)

nyzhuliping@gmail.com (Liping Zhu)

zhangzc@mail.xjtu.edu.cn (Zhengce Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-27-217, author = {Li , RuifeiZhu , Liping and Zhang , Zhengce}, 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} }
TY - JOUR T1 - Quenching Time for a Semilinear Heat Equation with a Nonlinear Neumann Boundary Condition AU - Li , Ruifei AU - Zhu , Liping AU - Zhang , Zhengce JO - Journal of Partial Differential Equations VL - 3 SP - 217 EP - 228 PY - 2014 DA - 2014/09 SN - 27 DO - http://doi.org/10.4208/jpde.v27.n3.3 UR - https://global-sci.org/intro/article_detail/jpde/5138.html KW - Nonlinear Neumann boundary KW - quenching KW - quenching time AB - 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.
Ruifei Li, Liping Zhu & Zhengce Zhang. (2019). Quenching Time for a Semilinear Heat Equation with a Nonlinear Neumann Boundary Condition. Journal of Partial Differential Equations. 27 (3). 217-228. doi:10.4208/jpde.v27.n3.3
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