Continuity of the quenching time in a semilinear heat equation with Neumann boundary condition

Abstract

This paper concerns the study of a semilinear parabolic equation subject to Neumann boundary conditions and positive initial datum. 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 datum. Finally, we give some numerical results to illustrate our analysis.

Keywords

• quenching
• semilinear parabolic equation
• numerical quenching time