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Continuity of the quenching time in a semilinear heat equation with a potential
Continuidad del tiempo de extinción en una ecuación semilineal de calor con potencial
Palabras clave:
Quenching, semilinear heat equation, numerical quenching time (en)Apagamiento, ecuación de calor semilineal, tiempo de apagamiento numérico (es)
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Abstract. 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.
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.
Referencias
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