Reviewing the mathematical validity of a fuel cell cathode model. Existence of weak bounded solution

We consider a system of nonlinear PDEs in a domain with a triple phase boundary, describing electrochemical processes in a mixed conduction, solid-oxide cathode of a fuel cell. It represents oxygen diffusion (with nonlinear diffusion coefficient) in the gas phase, oxygen ion diffusion in the bulk phase, electron diffusion in the electrolyte, surface exchange (nonlinear) on the interface of gas and the (mixed conduction) electrode material and finally charge transfer (nonlinear) at the interface between the electrolyte and the electrode material. We prove the validity of the model both mathematically and numerically. In fact, we prove the existence of a bounded weak solution using the Schauder fixed point theorem. We calculate the numerical solutions for given function and parameter values, and show that they correspond to theoretical results. In particular, we provide a numerical confirmation of the a priori bounds.