Non-local radiation conditions for the time-dependent Maxwell equations

Exact radiation conditions are proposed and proved for the time-dependent system of Maxwell equations, which describe the field in an unbounded domain with compact boundary and local sources. The conditions are specified on a sphere of finite, fixed radius, outside which the medium is an inhomogeneous dielectric. It is shown that the exact conditions may be reduced to approximate conditions, which are more convenient for numerical experimentation over large time intervals.