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

Claire Chainais-Hillairet; Ingrid Lacroix-Violet

doi:10.3934/dcdsb.2015.20.77

Article Contents

2015, Volume 20, Issue 1: 77-92. Doi: 10.3934/dcdsb.2015.20.77

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

Claire Chainais-Hillairet^1, and
Ingrid Lacroix-Violet^2,

1.
Laboratoire Paul Painlevé, CNRS UMR 8524, Université Lille 1, 59655 Villeneuve d'Ascq Cedex
2.
Laboratoire Paul Painlevé, CNRS-UMR 8524, Université Lille 1, 59655 Villeneuve d'Ascq Cedex

Received: February 28, 2014

Revised: February 28, 2014

Published: December 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 35A01, 35B45, 35B65, 35D30.

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