Continuity of the quenching time in a semilinear heat equation with Neumann boundary condition

Firmin K. N'gohisse; Théodore K. Boni

doi:10.33993/jnaat391-921

Authors

Firmin K. N'gohisse Université d'Abobo-Adjamé, Côte d'Ivoire
Théodore K. Boni Institut National Polytechnique Houphouet-Boigny de Yamoussoukro, Côte d'Ivoire

DOI:

https://doi.org/10.33993/jnaat391-921

Keywords:

quenching, semilinear parabolic equation, numerical quenching time

Abstract views: 271

Abstract

This paper concerns the study of a semilinear parabolic equation subject to Neumann boundary conditions 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 initial datum. Finally, we give some numerical results to illustrate our analysis.

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References

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