Global Lipschitz stability for inverse problems of wave equations on Lorentzian manifolds

We prove global Lipschitz stability for an inverse source problem of a system of wave equations on a Lorentzian manifold. The method used in this paper is widely known as the Bukhgeim-Klibanov method. However, the conventional method is not sufficient for the application to the hyperbolic partial differential equation with time-dependent coefficients to obtain the Lipschitz stability, and further innovations are needed. In this paper, we present an improved global Carleman estimate and an energy estimate to obtain the Lipschitz stability.& COPY; 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

Automated summary

We prove global Lipschitz stability for an inverse source problem of a system of wave equations on a Lorentzian manifold. The conventional method is not sufficient for the application to obtain the Lipschitz stability for the hyperbolic partial differential equation with time-dependent coefficients, and further innovations are needed. In this paper, we present an improved global Carleman estimate and an energy estimate to obtain the Lipschitz stability.