Numerical quenching for a semilinear parabolic equation with Dirichlet-Neumann boundary conditions and a potential
Théodore K. Boni, Thibaut K. Kouakou · 2009
This paper concerns the study of the numerical approximation for a semilinear parabolic equation with Dirichlet-Neumann boundary conditions and a potential. Under some conditions, we show that the solution of a semidiscrete form of the above problem quenches in a finite time and estimate its semidiscrete quenching time. We also establish the convergence of the semidiscrete quenching time, and finally, we give some numerical experiments to illustrate our analysis. u(x; 0) = u0(x) > 0; x2 (0; 1); (3) where f : (0;1)! (0;1) is a C 1 convex, nonincreasing function, R 0 ds f(s) 0, x2 (0; 1), b 0 (0) = 0, b 0 (1) = 0. The initial datum u02 C 2 ((0; 1)), u0(x) > 0, x2 (0; 1), u 00(x) b(x)f(u0(x)) < 0; x2 (0; 1); (4)