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

Maxime Breden (1) , Claire Chainais-Hillairet (2, 3) , Antoine Zurek (4)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 RAPSODI - Reliable numerical approximations of dissipative systems
3 LPP - Laboratoire Paul Painlevé - UMR 8524
4 Institute for Analysis and Scientific Computing [Wien]

The Diffusion Poisson Coupled Model describes the evolution of a dense oxide layer appearing at the surface of carbon steel canisters in contact with a claystone formation. It involves drift-diffusion equations on the density of species (electrons, ferric cations and oxygen vacancies), coupled with a Poisson equation on the electrostatic potential and with moving boundary equations. Traveling wave solutions are defined by stationary profiles on a fixed size domain with interfaces moving at the same velocity. In this paper, we present and apply a computer-assisted method in order to prove the existence of these traveling wave solutions. We also establish a precise and certified description of the solutions.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]

Maxime Breden, Claire Chainais-Hillairet, Antoine Zurek. Existence of traveling wave solutions for the Diffusion Poisson Coupled Model: a computer-assisted proof. 2020. ⟨hal-03082893v1⟩