Inverse problems for first-order hyperbolic equations with time-dependent coefficients
Analysis of PDEs
2025-03-14 v3
Abstract
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.
Cite
@article{arxiv.2009.12039,
title = {Inverse problems for first-order hyperbolic equations with time-dependent coefficients},
author = {Giuseppe Floridia and Hiroshi Takase},
journal= {arXiv preprint arXiv:2009.12039},
year = {2025}
}