Quenching Time of the Solution of a Semilinear Heat Equation in a Large Domain

Thodore K. Boni; Diabate Nabongo; Roger B. Sery

Quenching Time of the Solution of a Semilinear Heat Equation in a Large Domain

Thodore K. Boni ¹, Diabate Nabongo ², Roger B. Sery ³

Affiliations
1 Institut National Polytechnique, Houphout-boigny De Yamoussoukro, Bp 1093 Yamoussoukro, Côte d'Ivoire
2 Universit D'Abobo-Adjam, UFR-SFA, Dpartement De Mathma-Tiques et Informatiques, 16 Bp 372 Abidjan 16, Côte d'Ivoire
3 Institut National Polytechnique, Houphout-Boigny De Yamoussoukro, Bp 1093 Yamoussoukro, Côte d'Ivoire

In this paper, we consider a semilinear heat equation with Dirichlet boundary equation in a bounded domain. Under some assumptions, we show that the solution of the above problem quenches in a finite time and its quenching time goes to that of the solution of a certain differential equation when the size of the domain tends to infinity. Finally, we give some numerical experiments to illustrate our analysis.