R. Arancibia, R. Lecaros, A. Mercado, S. Zamorano (2022) An inverse problem for Moore-Gibson-Thompson equation arising in high intensity ultrasound, J. Inverse Ill-Posed Probl., Vol. 30, No. 5, pp. 659-675, 10.1515/jiip-2020-0090
Abstract. In this article, we study the inverse problem of recovering a space-dependent coefficient of the Moore–Gibson–Thompson (MGT) equation from knowledge of the trace of the solution on some open subset of the boundary. We obtain the Lipschitz stability for this inverse problem, and we design a convergent algorithm for the reconstruction of the unknown coefficient. The techniques used are based on Carleman inequalities for wave equations and properties of the MGT equation.