Totally discrete solution of the phenomenon of quenching for a localized heat equation

Author: 
Yoro.Gozo.,Halima.Nachid and L.B. Sobo Blin

In this paper we consider the following initial-boundary problem.

where is a convex, non-increasing function, for any real positif , , and We find some conditions under which the solution of a discrete form of the above problem quenches in a finite time and estimate its numerical quenching time. We also prove that the numerical quenching time converges to the real one when the mesh size goes to zero. Finally, we give some numerical results to illustrate our analysis.

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