CONTINUITY OF THE NUMERICAL QUENCHING TIME IN A SEMILINEAR HEAT EQUATION.

This paper concerns the study of the numerical approximation for the following initial-boundary value problem: u t = u xx - u -p , x ∊ (0, 1), t ∊ (0, T q ), u x (0, t) = 0, u x (1, t) = 0, t ∊ (0, T q ), u(x, 0) = u0(x) > 0, x ∊ [0, 1]. Under some assumptions, we prove that the solution of a semidiscrete form of the above problem quenches in a finite time and estimate its numerical quenching time. We also prove the continuity of the quenching time as a function of the initial datum. Finally, we give some numerical experiments to illustrate our analysis. [ABSTRACT FROM AUTHOR]

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