Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

OAI: https://revistas.ucr.ac.cr/index.php/matematica/oai
Existence of the weak solution for a stratified diffusion model via an iterative method
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Keywords

weak solution
Iterative method
non-linear diffusion
solución débil
método iterativo
difusión no lineal

How to Cite

Cano Macías, R., & Ruíz V., J. M. (2018). Existence of the weak solution for a stratified diffusion model via an iterative method. Revista De Matemática: Teoría Y Aplicaciones, 25(1), 151–168. https://doi.org/10.15517/rmta.v1i25.32235

Abstract

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.

https://doi.org/10.15517/rmta.v1i25.32235
PDF (Español (España))

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