Analysis of time-domain scattering by periodic structures

This paper is devoted to the mathematical analysis of a time-domain electromagnetic scattering by periodic structures which are known as diffraction gratings. The scattering problem is reduced equivalently into an initial-boundary value problem in a bounded domain by using an exact transparent boundary condition. The well-posedness and stability of the solution are established for the reduced problem. Moreover, a priori energy estimates are obtained with minimum regularity requirement for the data and explicit dependence on the time.