Quenching for a Semilinear Heat Equation With a Singular Boundary Outflux

Abstract

In this paper, we study the quenching behavior of solution of a semilinear heat equation with a singular boundary outflux. We first get a local existence result for this problem. We prove finite time quenching for the solution, we show that quenching occurs on the boundary and the time derivative blows up at the quenching time under certain conditions. Finally, we get a quenching rate and a lower bound for quenching time.