Existence result for degenerate cross-diffusion system with application to seawater intrusion

TL;DR

This paper establishes the existence of solutions for a strongly coupled degenerate parabolic system of porous medium type, with applications to modeling seawater intrusion, using entropy estimates to ensure solution properties.

Contribution

It provides a general existence proof for a class of degenerate cross-diffusion systems with applications to seawater intrusion models, without addressing uniqueness.

Findings

Existence of solutions proven for the degenerate system.

Entropy estimates control solution gradient and non-negativity.

Applicable to porous medium type models in seawater intrusion.

Abstract

In this paper, we study degenerate parabolic system, which are strongly coupled. We prove general existence result, but the uniqueness remains an open question. Our proof of existence is based on a crucial entropy estimate which both control the gradient of the solution and the non-negativity of the solution. Our system are of porous medium type and our method applies to models in seawater intrusion.