Continuity of the quenching time in a semilinear parabolic equation

In this paper, we consider the following initial-boundary value problem where is a bounded domain in RN with smooth boundary , p > 0, Δ is the Laplacian, v is the exterior normal unit vector on . Under some assumptions, we show that the solution of the above problem quenches in a finite time and estimate its quenching time. We also prove the continuity of the quenching time as a function of the initial data u0. Finally, we give some numerical results to illustrate our analysis.