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

Michel Cristofol (1, 2, 3, 4) , Patricia Gaitan (5) , Kati Niinimäki (6) , Olivier Poisson (7)

1 I2M - Institut de Mathématiques de Marseille
2 AMU - Aix Marseille Université
3 CNRS - Centre National de la Recherche Scientifique
4 ECM - École Centrale de Marseille
5 CPT - Centre de Physique Théorique - UMR 7332
6 Department of Applied Physics
7 LATP - Laboratoire d'Analyse, Topologie, Probabilités

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. 1. Introduction. Let Ω =]0, 1[, T > 0. We consider the following linear parabolic system:    

Domaines: Equations aux dérivées partielles [math.AP]

Michel Cristofol, Patricia Gaitan, Kati Niinimäki, Olivier Poisson. Inverse problem for a coupled parabolic system with discontinuous conductivities: One-dimensional case. Inverse Problems and Imaging , 2013, ⟨10.3934/ipi.2013.7.159⟩. ⟨hal-01264042⟩