Determining the conductivity for a non-autonomous hyperbolic operator in a cylindrical domain.

L. Beilina (1) , Michel Cristofol (2, 3, 4, 5) , S. Li (6)

1 Department of Mathematical Sciences
2 I2M - Institut de Mathématiques de Marseille
3 CNRS - Centre National de la Recherche Scientifique
4 AMU - Aix Marseille Université
5 ECM - École Centrale de Marseille
6 Wu Wen-Tsun Key Laboratory of Mathematics, Chinese Academy of Sciences

This paper is devoted to the reconstruction of the conductivity coefficient for a nonautonomous hyperbolic operator an infinite cylindrical domain. Applying a local Carleman estimate, we prove the uniqueness and a Hölder stability in the determination of the conductivity using a single measurement data on the lateral boundary. Our numerical examples show good reconstruction of the location and contrast of the conductivity function in 3 dimensions.

Mots clés: inverse problem; Carleman estimate; infinite domain; hyperbolic equations; time and space-dependent coefficient

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [cs.NA]

L. Beilina, Michel Cristofol, S. Li. Determining the conductivity for a non-autonomous hyperbolic operator in a cylindrical domain.. Mathematical Methods in the Applied Sciences, 2018, 41 (5), pp.2012-2030. ⟨10.1002/mma.4728⟩. ⟨hal-01479160⟩