Degenerate Convection-Diffusion Equation with a Robin boundary condition

TL;DR

This paper investigates a degenerate convection-diffusion equation with Robin boundary conditions, establishing existence and uniqueness of entropy solutions, and illustrating solution behaviors through numerical simulations and experiments.

Contribution

It introduces a new framework for entropy solutions in degenerate convection-diffusion equations with Robin boundaries, including existence and uniqueness results.

Findings

Existence and uniqueness of entropy solutions proven.

Numerical simulations demonstrate solution behaviors.

Monodimensional experiments validate theoretical results.

Abstract

We study a Robin boundary problem for degenerate parabolic equation. We suggest a notion of entropy solution and propose a result of existence and uniqueness. Numerical simulations illustrate some aspects of solution behaviour. Monodimensional experiments are presented.