Carleman estimates and some inverse problems for the coupled quantitative thermoacoustic equations by boundary data. Part II: some inverse problems

Estimations de Carleman et problèmes inverses pour le système thermoacoustique couplé à partir d'observations au bord du domaine. Partie II : quelques problèmes inverses

Michel Cristofol (1, 2, 3, 4) , Shumin Li (5) , Yunxia Shang (6)

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 School of Mathematical Sciences
6 SHNU - Shanghai Normal University

In this paper, we consider Carleman estimates and inverse problems for the coupled quantitative thermoacoustic equations. In the previous Part I of this paper, we established Carleman estimates for the coupled quantitative thermoa-acoustic equations by assuming that the coefficients satisfy suitable conditions. We apply Carleman estimates in the previous Part I to some inverse problems for the coupled quantitative thermoacoustic equations and prove stability estimates of the Hölder type.

Mots clés: Inverse problems; thermoacoustic equations; coupled; coupled 2010 Mathematics Subject Classfication 35R30

Domaines: Equations aux dérivées partielles [math.AP]

Michel Cristofol, Shumin Li, Yunxia Shang. Carleman estimates and some inverse problems for the coupled quantitative thermoacoustic equations by boundary data. Part II: some inverse problems. Mathematical Methods in the Applied Sciences, 2023, 46 (12), pp.13304-13319. ⟨10.1002/mma.9252⟩. ⟨hal-02863385⟩