Lipschitz stability for an inverse hyperbolic problem of determining two coefficients by a finite number of observations

L. Beilina (1) , Michel Cristofol (2, 3, 4, 5) , S. Li (6, 7) , M Yamamoto (8)

1 Chalmers - Department of Mathematical Sciences
2 I2M - Institut de Mathématiques de Marseille
3 AMU - Aix Marseille Université
4 CNRS - Centre National de la Recherche Scientifique
5 ECM - École Centrale de Marseille
6 Wu Wen-Tsun Key Laboratory of Mathematics, Chinese Academy of Sciences
7 USTC - University of Science and Technology of China [Hefei]
8 UTokyo - The University of Tokyo

We consider an inverse problem of reconstructing two spatially varying coefficients in an acoustic equation of hyperbolic type using interior data of solutions with suitable choices of initial condition. Using a Carleman estimate, we prove Lipschitz stability estimates which ensure unique reconstruction of both coefficients. Our theoretical results are justified by numerical studies on the reconstruction of two unknown coefficients using noisy backscattered data.

Mots clés: algorithm; coefficient inverse problem; Carleman estimate; an acoustic; equation of hyperbolic type; adaptive; two space-dependent coefficients

Domaines: Equations aux dérivées partielles [math.AP]

L. Beilina, Michel Cristofol, S. Li, M Yamamoto. Lipschitz stability for an inverse hyperbolic problem of determining two coefficients by a finite number of observations. Inverse Problems, 2018, 34 (1), ⟨10.1088/1361-6420/aa941d⟩. ⟨hal-01714738⟩