A coupling and modeling of sediment transport in coastal environments

This paper presents a mathematical analysis of a coupled system for modeling sediment transport and dune evolution in coastal environments. The model combines the Shallow Water Equations (SWE) with the Long-Term Dune Dynamics (LTDD) equation, incorporating viscosity and modified pressure terms. Using methods of mathematical analysis, we prove the existence and uniqueness of solutions for the system. We also provide estimates for its dimensionless form and conclude by presenting a homogenized version of the combined model.