Continuity of the quenching time in a semilinear parabolic equation with variable exponent

Author:

Théodore Kouassi BONI, Remi Kouadio KOUAKOU

2010 Mathematics Subject Classication:

5B40, 35B50, 35K60, 65M06

Keywords:

numerical quenching time, quenching, semilinear parabolic equation

Abstract:

This paper concerns the study of a semilinear parabolic equation with variable exponent subject to Neumann boundary conditions and positive initial datum. 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 initial datum. Finally, we give some numerical results to illustrate our analysis.

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Boni-Koua-2011

Vol. 6 (14), 2011