On the existence of solutions for a drift-diffusion system arising in corrosion modelling

TL;DR

This paper proves the existence of weak solutions for a coupled drift-diffusion system modeling corrosion in nuclear waste repositories, highlighting unique boundary conditions compared to semiconductor models.

Contribution

It introduces a novel corrosion model with Robin boundary conditions and establishes solution existence via semi-discretization techniques.

Findings

Existence of weak solutions for the corrosion drift-diffusion system

Novel boundary conditions induce additional coupling

Method applicable to similar coupled PDE systems

Abstract

In this paper, we consider a drift-diffusion system describing the corrosion of an iron based alloy in a nuclear waste repository. In comparison with the classical drift-diffusion system arising in the modeling of semiconductor devices, the originality of the corrosion model lies in the boundary conditions which are of Robin type and induce an additional coupling between the equations. We prove the existence of a weak solution by passing to the limit on a sequence of approximate solutions given by a semi-discretization in time.