Quenching for a reaction-diffusion equation with weak singularities

Abstract

This paper studies the following reaction-diffusion equation with a weak singular boundary condition. The primary objective for this problem is to analyze the quenching properties. It is obtained that finite time quenching occurs on the left boundary, the time derivative of the solution blows up at the same time and also quenching rate estimates of the solution of the eqaution kt(x, t) = kxx(x, t) + ln ?k(x, t), (x, t) ? (0, 1) × (0, T) with kx (0, t) = ? ln ?k(0, t), kx (1, t) = 0, t ? (0, T) and initial function k (x, 0) = k0 (x) with [0, 1] ? (0, 1) where 0 < ?, ? < 1 and T is a finite time.