EXISTENCE OF THE WEAK SOLUTION FOR A STRATIFIED DIFFUSION MODEL VIA AN ITERATIVE METHOD

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.

Keywords

• solución débil
• método iterativo
• difusión no lineal