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

Abstract

This paper is concerned with the determination of coefficients and source term in a strong coupled quantitative thermoacoustic system of equations. Adapting a Carleman estimate established in the part I of this series of papers, we prove stability estimates of Hölder type involving the observation of only one component: the temperature or the pressure.

Recovering coefficients in a system of semilinear Helmholtz equations from internal data

“…The proof of the above uniqueness result is constructive in the sense that it provides an explicit way to solve the inverse problem: solving (18) for u 1 , computing q using (19) and then computing Γ as in (20).…”

“…The proportional constant Γ(x) is called the Grüneisen coefficient [10]. We refer interested readers to [3,12,13,20] and references therein for the recent development in the modeling and computational aspects of thermoacoustic imaging.…”