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

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Authors

  • Institut National Polytechnique, Houphout-Boigny De Yamoussoukro, Bp 1093 Yamoussoukro ,CI
  • Universit D'Abobo-Adjam, UFR-SFA, Departement De Mathma-Tiques et Informatiques, 16 Bp 372, Abidjan 16 ,CI
  • Institut National Polytechnique, Houphout-Boigny De Yamoussoukro, Bp 1093 Yamoussoukro ,CI

Keywords:

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

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.