1Institut National Polytechnique Houphouët-Boigny de Yamoussoukro, Abidjan, Côte d'Ivoire. Email: theokboni@yahoo.fr
2Université d'Abobo-Adjamé, UFR-SFA, Abidjan, Côte d'Ivoire. Email: kkthibaut@yahoo.fr
In this paper, we consider a semilinear heat equation with a potential subject to Neumann boundary conditions and positive initial data. 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 potential and the initial data. Finally, we give some numerical results to illustrate our analysis.
Key words: Quenching, semilinear heat equation, numerical quenching time.
En este trabajo consideramos una ecuación semilineal de calor con potencial, sujeta a condiciones de Neumann de frontera y datos iniciales positivos. Bajo ciertos supuestos mostramos que la solución de dicha ecuación se apaga en tiempo finito y estimamos el tiempo en que lo hace. También probamos la continuidad del tiempo de extinción en función del potencial y de los datos iniciales. Finalmente damos algunos resultados numéricos que ilustran nuestro análisis.
Palabras clave: Apagamiento, ecuación de calor semilineal, tiempo de apagamiento numérico.
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References
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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCMv43n1a06, ]]>
AUTHOR = {Boni, Théodore K. and Kouakou, Thibaut K.},
TITLE = {{Continuity of the quenching time in a semilinear heat equation with a potential}},
JOURNAL = {Revista Colombiana de Matemáticas},
YEAR = {2009},
volume = {43},
number = {1},
pages = {55-70}
}