Lipschitz stability for an inverse source problem of the wave equation with kinetic boundary conditions
Abstract
In this paper, we present a refined approach to establish a global Lipschitz stability for an inverse source problem concerning the determination of forcing terms in the wave equation with mixed boundary conditions. It consists of boundary conditions incorporating a dynamic boundary condition and Dirichlet boundary condition on disjoint subsets of the boundary. The primary contribution of this article is the rigorous derivation of a sharp Carleman estimate for the wave system with a dynamic boundary condition. In particular, our findings complete and drastically improve the earlier results established by Gal and Tebou [SIAM J. Control Optim., 55 (2017), 324-364]. This is achieved by using a different weight function to overcome some relevant difficulties. As for the stability proof, we extend to dynamic boundary conditions a recent argument avoiding cut-off functions. Finally, we also show that our developed Carleman estimate yields a sharp boundary controllability result.
Keywords
Cite
@article{arxiv.2402.12902,
title = {Lipschitz stability for an inverse source problem of the wave equation with kinetic boundary conditions},
author = {S. E. Chorfi and G. El Guermai and L. Maniar and W. Zouhair},
journal= {arXiv preprint arXiv:2402.12902},
year = {2026}
}
Comments
Accepted in SIAM Journal on Control and Optimization