Annales Mathématiques Africaines

On Quenching and Continuity of The Quenching Time for a Semilinear Parabolic Equation

Rémi K. Kouakou
UFR-SFA Laboratoire de Mathématiques et Informatiques
Université Nangui Abrogoua
02 BP 801 Abidjan 02, Côte d’Ivoire

Mathematics Subject Classification: (2010) 35B40, 45A07, 45G10, 65M06
Key words: Quenching, nonlinear parabolic equation, numerical quenching time.

Abstract:

This paper concerns the study of a semilinear parabolic equation subject to Neumann boundary conditions, with variable reaction 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 nonlinear source. Finally, we give some numerical results to illustrate our analysis.