Existencia global y explosión de la solución de un problema de difusión - reacción
DOI:
https://doi.org/10.17268/sel.mat.2017.01.09Palavras-chave:
problema de difusión - reacción, existencia global, existencia local, solución explosiva, tiempo de exposiónResumo
En este artículo se hace un estudio analítico sobre la existencia global y local de la solución de un problema de difusión - reacción. Se demuestra que si la solución existe localmente entonces
esta llega a explotar en tiempo finito. Este resultado se extiende al caso en que la solución exista globalmente. Se llega a concluir que el tiempo máximo de existencia de la solución depende del dominio, del término que representa la reacción en la ecuación y de una función prueba definida en este trabajo. Así mismo se plantea la posibilidad de extender la existencia local a global usando el concepto de solución propia.
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