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

Impact Factor:1.1

DOI number:10.1515/jiip-2020-0045

Journal:Journal of Inverse and Ill-Posed Problems

Key Words:Carleman estimates; thermoacoustic equations; coupled; inverse problems

Abstract:In this paper, we consider Carleman estimates and inverse problems for the coupled quantitative thermoacoustic equations. In part I, we establish Carleman estimates for the coupled quantitative thermoacoustic equations by assuming that the coefficients satisfy suitable conditions and taking the usual weight function φ(x, t) = e^{λψ(x,t)}, ψ(x, t) = |x − x_0|^2 − β|t − t_0|^2 + βt^2_0 for x in a bounded domain in ℝn with C^3-boundary and t ∈ (0, T), where t0 =T/2. We will discuss applications of the Carleman estimates to some inverse problems for the coupled quantitative thermoacoustic equations in the succeeding part II paper [M. Cristofol, S. Li and Y. Shang, Carleman estimates and inverse problems for the coupled quantitative thermoacoustic equations. Part II: Inverse problems, preprint (2020), https://hal.archives-ouvertes.fr/hal-02863385].

Co-author:Shumin Li,Yunxia Shang

Indexed by:Journal paper

Document Code:000762443900001

Discipline:Natural Science

Document Type:J

Volume:30

Issue:5

Page Number:621-658

ISSN No.:0928-0219

Translation or Not:no

Date of Publication:2022-10-01

Included Journals:SCI、EI

Links to published journals:https://doi.org/10.1515/jiip-2020-0045