No abstract

Abstract. In this paper, we consider the following initial-boundary value problemwhere Ω is a bounded domain in R N with smooth boundary ∂Ω, p > 0, ∆ is the Laplacian, ν is the exterior normal unit vector on ∂Ω. 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.

In this paper, under certain conditions, we show that the solution of the semidiscrete form of a semilinear heat equation with a variable reaction is quenched in a finite time and estimate its semidiscrete quenching time. We also show that the semidiscrete quenching time converges to the continuous one when the mesh size goes to zero. In the same way, an analogous study has been investigated taking into account the discrete form of the above problem. Finally, we present some computational results.