  Consider the time-domain multiple cavity scattering problem, which arises in
diverse scientific areas and has significant industrial and military
applications. The multiple cavity embedded in an infinite ground plane, is
filled with inhomogeneous media characterized by variable dielectric
permittivities and magnetic permeabilities. Corresponding to the transverse
electric or magnetic polarization, the scattering problem can be studied for
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 are
established for the reduced problem. Moreover, a priori estimates for the
electric field is obtained with a minimum requirement for the data by directly
studying the wave equation.
