Analysis of Time-domain Electromagnetic Scattering Problem by Multiple Cavities

The time-domain multiple cavity scattering problem, which arises in diverse scientific areas, has significant industrial and military applications. The multiple cavities, embedded in an infinite ground plane, is filled with inhomogeneous media characterized by variable dielectric permittivities and magnetic permeabilities. Corresponding to the transverse electric, the scattering problem can be studied by the Helmholtz equation in frequency domain and wave equation in time-domain respectively. A novel transparent boundary condition in time-domain is developed to reformulate the cavity scattering problem into an initial-boundary value problem in a bounded domain. The well-posedness and stability of the reduced problem are established. Moreover, a priori energy estimates for the electric field is obtained with minimum regularity requirement for the data and an explicit dependence on the time by studying the wave equation directly.