Existencia global y explosión de la solución de un problema de difusión - reacción
- Autores: Julio José Augusto Becerra Saucedo
- Localización: Selecciones Matemáticas, ISSN-e 2411-1783, Vol. 4, Nº. 1, 2017 (Ejemplar dedicado a: Enero - Julio), págs. 82-101
- Idioma: español
- DOI: 10.17268/sel.mat.2017.01.09
- Títulos paralelos:
- Global existence and blow up of the solution of a problem diffusion - reaction
- Enlaces
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Resumen
- español
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 entoncesesta 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.
- English
This article presents an analytical study on the local and global existence of the solution of diffusion - reaction problem. We show that if the solution exists locally then, it blows up in finite time. This result covers the case that the solution exists globally. We concluded that the maximum time of existence of the solution depends on the domain, the term representing the reaction in the equation and a test function defined in this job. Likewise we propose the possibility of extending the local existence to the global one using the proper solution framework.
- español
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