Continuity of the quenching time in a semilinear heat equation with a potential

in this paper, we consider a semilinear heat equation with a potential subject to neumann boundary conditions and positive initial data. 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 potential and the initial data. finally, we give some numerical results to illustrate our analysis.