Existence of traveling wave solutions for the Diffusion Poisson Coupled Model: a computer-assisted proof

The Diffusion Poisson Coupled Model describes the evolution of a dense oxide layer appearing at surface carbon steel canisters in contact with claystone formation. This model is one dimensional free boundary problem involving drift-diffusion equations on density species (electrons, ferric cations and oxygen vacancies), coupled equation electrostatic potential moving equations, which describe position each unknown interfaces spatial domain. Numerical simulations suggest existence traveling wave solutions for this model. These are defined by stationary profiles fixed size domain both same velocity. In paper, we present apply computer-assisted method order to prove these solutions. We also establish precise certified description