Inverse problem for a coupled parabolic system with discontinuous conductivities: One-dimensional case

Michel Cristofol; Patricia Gaitan; Kati Niinimäki; Olivier Poisson

doi:10.3934/ipi.2013.7.159

Article Contents

2013, Volume 7, Issue 1: 159-182. Doi: 10.3934/ipi.2013.7.159

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Inverse problem for a coupled parabolic system with discontinuous conductivities: One-dimensional case

1.
Aix-Marseille Universite, LATP, Technopôle Château-Gombert, 39, rue F. Joliot Curie, 13453 Marseille Cedex 13
2.
Aix-Marseille Universite, CPT, Campus de Luminy, Case 907, 13288 Marseille cedex 9
3.
Department of Applied Physics, University of Eastern Finland, Kuopio campus, P.O.Box 1627, FIN-70211 Kuopio

Received: March 2012

Revised: November 2012

Published: February 2013

Abstract / Introduction Related Papers Cited by

Abstract

We study the inverse problem of the simultaneous identification of two discontinuous diffusion coefficients for a one-dimensional coupled parabolic system with the observation of only one component. The stability result for the diffusion coefficients is obtained by a Carleman-type estimate. Results from numerical experiments in the one-dimensional case are reported, suggesting that the method makes possible to recover discontinuous diffusion coefficients.

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Mathematics Subject Classification: Primary: 35R30, 35K57, 90C20, 90C51.

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