NUMERICAL QUENCHING OF A SEMILINEAR HEAT EQUATION WITH A SINGULAR BOUNDARY OUTFLUX

Abstract

In this paper, we study the semidiscrete approximation for the following semilinear heat equation with a singular boundary outflux \uf8f1\uf8f4\uf8f2\uf8f4\uf8f4\uf8f3 ∂u ∂t = uxx + (1− u)−p, 0 < x < 1, t > 0, ux(0, t) = 0, ux(1, t) = −u(1, t)−q, t > 0, u(x, 0) = u0(x), 0 ≤ x ≤ 1. . We find some conditions under which the solution of a semidiscrete form of above problem quenches in a finite time and estimate its semidiscrete quenching time. We also establish the convergence of the semidiscrete quenching time to the theoretical one when the mesh size tends to zero. Finally, we give some numerical experiments for a best illustration of our analysis.