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.