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Quenching for semidiscretizations of a semilinear heat equation with Dirichlet and Neumann boundary conditions

Diabate Nabongo;  Théodore K. Boni — 2008

Commentationes Mathematicae Universitatis Carolinae

This paper concerns the study of the numerical approximation for the following boundary value problem: u t ( x , t ) - u x x ( x , t ) = - u - p ( x , t ) , 0 < x < 1 , t > 0 , u x ( 0 , t ) = 0 , u ( 1 , t ) = 1 , t > 0 , u ( x , 0 ) = u 0 ( x ) > 0 , 0 ≤ x ≤ 1 , where p > 0 . We obtain some conditions under which 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. Finally, we give some numerical experiments to illustrate our analysis.

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