The existence of solutions to a corrosion model

In this work, we consider a corrosion model of iron based alloy in a nuclear waste repository. It consists of a PDE system, similar to the steady-state drift-diffusion system arising in semiconductor modelling. The main difference lies in the boundary conditions, since they are Robin boundary conditions and imply an additional coupling between the equations. Using a priori estimates for the solution and Schauder's fixed point theorem, we show the existence of solutions to the corrosion model.