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On the existence of solutions for a drift-diffusion system arising in corrosion modeling. (English) Zbl 1304.35331

Summary: 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.

MSC:

35K51 Initial-boundary value problems for second-order parabolic systems
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35B45 A priori estimates in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
35D30 Weak solutions to PDEs
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References:

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