Singularly perturbed degenerated parabolic equations and application to seabed morphodynamics in tided environment

TL;DR

This paper develops and analyzes models for seabed morphodynamics in tidal environments using singularly perturbed degenerated parabolic equations, providing existence, uniqueness, and homogenization results for different time scales.

Contribution

It introduces novel models for seabed morphodynamics based on degenerated and singularly perturbed parabolic equations, with proven existence, uniqueness, and homogenization results.

Findings

Existence and uniqueness of solutions for short-term and mean-term models.

Homogenization of the short-term model.

Development of models for various time scales of seabed morphodynamics.

Abstract

In this paper we build models for short-term, mean-term and long-term dynamics of dune and megariple morphodynamics. They are models that are degenerated parabolic equations which are, moreover, singularly perturbed. We, then give an existence and uniqueness result for the short-term and mean-term models. This result is based on a time-space periodic solution existence result for degenerated parabolic equation that we set out. Finally the short-term model is homogenized.