Abstract

CANO MACIAS, Ricardo  and  RUIZ V., Jorge Mauricio. Existence of the weak solution for a Stratified diffusion model via an iterative method. Rev. Mat [online]. 2018, vol.25, n.1, pp.151-168. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v1i25.32235.

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.

        · abstract in Spanish     · text in Spanish     · Spanish ( pdf )