# American Institute of Mathematical Sciences

February  2013, 7(1): 159-182. doi: 10.3934/ipi.2013.7.159

## 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, France, France 2 Aix-Marseille Universite, CPT, Campus de Luminy, Case 907, 13288 Marseille cedex 9, France 3 Department of Applied Physics, University of Eastern Finland, Kuopio campus, P.O.Box 1627, FIN-70211 Kuopio, Finland

Received  March 2012 Revised  November 2012 Published  February 2013

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.
Citation: Michel Cristofol, Patricia Gaitan, Kati Niinimäki, Olivier Poisson. Inverse problem for a coupled parabolic system with discontinuous conductivities: One-dimensional case. Inverse Problems & Imaging, 2013, 7 (1) : 159-182. doi: 10.3934/ipi.2013.7.159
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