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

Claire Chainais-Hillairet (1) , Ingrid Lacroix-Violet (1)

1 RAPSODI - Reliable numerical approximations of dissipative systems

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.

Mots clés: Drift-di usion system; Robin boundary conditions; Existence of weak solutions; A priori estimates

Domaines: Equations aux dérivées partielles [math.AP]

Claire Chainais-Hillairet, Ingrid Lacroix-Violet. On the existence of solutions for a drift-diffusion system arising in corrosion modelling. Discrete and Continuous Dynamical Systems - Series B, 2015, 20 (1), pp.77-92. ⟨10.3934/dcdsb.2015.20.77⟩. ⟨hal-00764239⟩