The Journal of the Indian Mathematical Society

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

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

Abstract

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.

Keywords

Quenching, Finite Difference, Semilinear Heat Equation, Numerical Quenching Time, Convergence.

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