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

Solvability for a drift-diffusion system with Robin boundary conditions

“…Nevertheless, due to the special properties of the 1-D Laplace operator, our results apply to the one dimensional Debye type system considered in [7], a problem we had primarily in view (see also [1]). In that case, our existence result improves the former result in [7]. Actually, since we work in a L 2 frame and remove the sign condition of the Debye 2 × 2 system, we obtain an existence result for a general n × n system (d = 1).…”

“…Then we illustrate this general setting with more specific model, namely the corrosion modeling in a nuclear waste repository (cf. [1,7]).…”

“…Actually, since we work in a L 2 frame and remove the sign condition of the Debye 2 × 2 system, we obtain an existence result for a general n × n system (d = 1). We also remove the restrictive conditions on the initial data in [7]. Finally, to conclude this section, note that in the case B = ∆ −1 D , d ≥ 2, a mollifying process can be used on B in order to recover some classical results of the theory.…”

Study of a pseudo-stationary state for a corrosion model: Existence and numerical approximation

“…The main difficulties are of three types: the system is strongly coupled (the coupling arises in the equations and in the boundary conditions), the boundary conditions are Robin boundary conditions and the interfaces are moving. In [9], ChainaisHillairet and Lacroix-Violet proves the existence of a solution in a simplified case where only electrons and cations are taken into account and therefore the domain is fixed. Convergence of backward Euler scheme in time and finite volume scheme in space for the same simplified system has been established in [7].…”

Convergence of a Finite Volume Scheme for a Corrosion Model

“…In this paper we focus on the simplified corrosion model already introduced in [1, 11]. The unknowns of the model are the densities of electrons N and cations Fe 3+ P and the electric potential Ψ.…”