A Mathematical Study of a Hyperbolic Metamaterial in Free Space

Wave propagation in hyperbolic metamaterials is described by the Maxwell equations with a frequency-dependent tensor of dielectric permittivity, whose eigenvalues are different signs. In this case problem becomes (Klein--Gordon equation) for certain range frequencies. The principal theoretical and numerical difficulty comes from fact that equation posed free space, without initial conditions provided. subject work justification problem. particular, includes construction radiation condition, well-posedness result, limiting absorption principle, regularity estimates on solution.