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Electromagnetic Scattering for Time-Domain Maxwell's Equations in an Unbounded Structure

The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell's equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an initial-boundary value problem in an infinite rectangular slab. The well-posedness and stability are established for the reduced problem. Our proof is based on the method of energy, the Lax--Milgram lemma, and the inversion theorem of the Laplace transform. Moreover, a priori estimates with explicit dependence on the time are achieved for the electric field by directly studying the time-domain Maxwell equations.