Homogenization and transport equations: the case of desert and sand piles

TL;DR

This paper develops and analyzes homogenization models for the short-term, mean-term, and long-term dynamics of dunes in deserts, addressing degenerated and singularly perturbed parabolic equations.

Contribution

It introduces new homogenization and corrector results for complex degenerated and singularly perturbed models of dune dynamics.

Findings

Existence and uniqueness of solutions established.

Homogenization results derived for the models.

Corrector results provided for the models.

Abstract

In this paper we build models for short-term, mean-term and long-term dynamics of dune in desert. They are models that are degenerated parabolic equations which are, moreover, singularly perturbed. We, then give existence and uniqueness results for the models, followed by homogenization ones and a corrector result is given.