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