Quenching for a nonlinear diffusion equation with a singular boundary condition

Abstract. We study a nonlinear diffusion equation $(\psi (u))_t =u_{xx},\0 < x < 1,\t > 0$ with a singular boundary condition $u_x(1,t) = -g(u(1,t))$. We prove finite time quenching for the solution. We also establish results on quenching set and rate.