The Maxwell system in nonhomogeneous anisotropic waveguides with slowly stabilizing characteristics of filling medium

In a region with a finite number of cylindrical exits to infinity, a stationary Maxwell system with ideally conducting boundary conditions is investigated. It is assumed that the dielectric and magnetic permittivity are arbitrary positive definite matrix functions with slow stabilization at infinity. A scattering matrix is introduced, a unique solvability of the problem with radiation conditions at infinity is established, and the asymptotics of solutions are described.