Inverse problems for first-order hyperbolic equations with time-dependent coefficients

We prove global Lipschitz stability for inverse source and coefficient problems for first-order linear hyperbolic equations, the coefficients of which depend on both space and time. We use a global Carleman estimate, and a crucial point, introduced in this paper, is the choice of the length of integral curves of a vector field generated by the principal part of the hyperbolic operator to construct a weight function for the Carleman estimate. These integral curves correspond to the characteristic curves in some cases. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

The study proves global Lipschitz stability for inverse source and coefficient problems of first-order linear hyperbolic equations, where the key lies in choosing the length of integral curves to construct a weight function for the Carleman estimate. These integral curves correspond to characteristic curves in certain cases.