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Original scientific paper

Extinction time for some nonlinear heat equations

Louis A. Assalé ; Institut National Polytechnique Houphouët-Boigny de Yamoussoukro, Yamoussoukro, Côte d'Ivoire
Théodore K. Boni
Diabate Nabongo


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Abstract

This paper concerns the study of the extinction time of the solution of the following initial-boundary value problem
Extra \left or missing \right
where Ω is a bounded domain in RN with smooth boundary Ω, ε is a positive parameter, f(s) is a positive, increasing, concave function for positive values of s, f(0)=0, 0dsf(s)<+, L is an elliptic operator. We show that the solution of the above problem extincts in a finite time and its extinction time goes to that of the solution α(t) of the following differential equation
α(t)=f(α(t)),t>0,α(0)=M, as
ε goes to zero, where M=supxΩu0(x).
We also extend the above result to other classes of nonlinear
parabolic equations. Finally, we give some numerical results to
illustrate our analysis.

Keywords

extinction; finite difference; nonlinear heat equations; extinction time

Hrčak ID:

30900

URI

https://hrcak.srce.hr/30900

Publication date:

23.12.2008.

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