Abstract
In this article, we prove stability estimate of the inverse problem of determining the magnetic field entering the magnetic wave equation in a bounded smooth domain in ℝ d from boundary observations. This information is enclosed in the hyperbolic (dynamic) Dirichlet-to-Neumann map associated to the solutions to the magnetic wave equation. We prove in dimension d ≥ 2 that the knowledge of the Dirichlet-to-Neumann map for the magnetic wave equation measured on the boundary determines uniquely the magnetic field and we prove a Hölder-type stability in determining the magnetic field induced by the magnetic potential.
Acknowledgement
The authors thank the anonymous referee for very useful comments.