Reconstruction of a time dependent source term from a single boundary measurement in Maxwell's equations with nonlinear generalized Ohm's law

Hyperbolic Maxwell's equation with an unknown time dependent source is investigated. We consider a nonlinear generalized Ohm's law in our model. The source is reconstructed from a single boundary measurement over a part of the boundary. We use well-known Rothe's method to show the existence of a solution. In the case of regular solution, we provide a uniqueness proof as well. To support theoretical results a numerical experiment is provided.