Determination of a time-dependent convolution kernel from a boundary measurement in nonlinear Maxwell's equations

A nonlinear hyperbolic Maxwell equation with an unknown solely time dependent convolution kernel is studied. The missing kernel is recovered from an additional normal component measurement over the whole boundary. The existence of a solution to this inverse problem is shown. Moreover a constructive algorithm for approximations is designed and its convergence is established. Uniqueness is proved for a regular solution. Theoretical results are supported by a numerical experiment.