2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74913We study Maxwell's equations in time domain in an anisotropic medium. The goal of the paper is to solve an inverse boundary value problem for anisotropies characterized by scalar impedance $α$. This means that the material is conformal, i.e., the electric permittivity $ε$ and magnetic permeability $μ$ are tensors satisfying $μ=α^2ε$. This condition is equivalent to a single propagation speed of waves with different polarizations which uniquely defines an underlying Riemannian structure. The analysis is based on an invariant formulation of the system of electrodynamics as a Dirac type first order system on a Riemannian $3-$manifold with an additional structure of the wave impedance, $(M,g,α)$, where $g$ is the travel-time metric. We study the properties of this system in the first part of the paper. In the second part we consider the inverse problem, that is, the determination of $(M,g,α)$ from measurements done only on an open part of the boundary and on a finite time interval. As an application, in the isotropic case with $M\subset \R^3$, we prove that the boundary data given only on an open part of the boundary determine uniquely the domain $M$ and the coefficients $ε$ and $μ$.Analysis of PDEs58J45, 35R30, 35Q60text