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Revista de Matemática Teoría y Aplicaciones
Print version ISSN 1409-2433
Rev. Mat vol.25 n.1 San José Jan./Jun. 2018
http://dx.doi.org/10.15517/rmta.v1i25.32235
Artículos
Existencia de la solución débil de un Modelo de difusión estratificada vía un método iterativo
Existence of the weak solution for a Stratified diffusion model via an iterative method
1Facultad de Ingeniería, Universidad de La Sabana, Chía, Colombia. E-Mail: ricardocm@unisabana.edu.co
2Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá D.C., Colombia. E Mail: jmruizv@unal.edu.co
Se estudia la existencia y unicidad de la solución débil de un problema de difusión estratificada no lineal. Para ésto, se construye un método alternativo basado en sustituciones sucesivas de una aproximación lineal del problema original. Empleando la teoría de ecuaciones diferenciales parciales y usando inducción matemática se prueba que cada uno de los problemas lineales de la iteración tiene una única solución débil, obteniendo así, una sucesión de soluciones débiles. Finalmente, se demuestra que dicha suseción es de Cauchy y que converge a la solución débil del problema.
Palabras clave: solución débil; método iterativo; difusión no lineal
We study the existence and uniqueness of the solution of a non-linear stratified diffusion problem. To this aim, we construct an alternative method based on successive substitutions of a linear approximation of the original problem. We use the theory of partial differential equations and mathematical induction to prove that each of the linear problems of the iteration has a unique weak solution. Finally, we prove that the sequence of weak solutions obtained is a Cauchy sequence that converges to the weak solution of the problem.
Keywords: weak solution; Iterative method; non-linear diffusion
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Recibido: 07 de Junio de 2017; Revisado: 05 de Diciembre de 2017; Aprobado: 06 de Diciembre de 2017
Este es un artículo publicado en acceso abierto bajo una licencia Creative Commons
