An identification problem for the Maxwell equations in a non-homogeneous dispersive medium
We consider the propagation of electromagnetic waves in a non-homogeneous medium. The related constitutive relations contain time and space dependent convolution kernels. Since they are a priori unknown, a basic question concerns their identification. In the present paper, this is obtained by reducing the problem to a system of nonlinear integral equations of the second kind. Via a Contraction Theorem, we prove local (in time) existence and uniqueness results. Lipschitz continuous dependence upon the data is also proved. © 1995, Khayyam Publishing.
Differential and Integral Equations
Cavaterra, C., Lorenzi, A., & Goldstein, J. (1995). An identification problem for the Maxwell equations in a non-homogeneous dispersive medium. Differential and Integral Equations, 8 (5), 1167-1190. Retrieved from https://digitalcommons.memphis.edu/facpubs/4176