Quenching for A Nonlinear Diffusion Equation with Singular Boundary Outfluxes

Abstract

In this paper, we study a nonlinear diffusion equation (φ(u))t = uxx, 0 0 with singularboundary outfluxes ux(0, t) = u−p(0, t), ux(a, t) = −u−q(a, t). Firstly, we get the quenching occurs in a finite time atthe boundary x = a under certain conditions. Finally, we show the time derivative blows up at the quenching timeand we also establish results on quenching time and rate for certain nonlinearities.