Unique solvability and stability of the time domain electromagnetic scattering problem with a locally perturbed perfectly conducting plate

Abstract

In this paper, we investigate the unique solvability and stability of the time domain electromagnetic scattering problem with a kind of unbounded scatterer, that is, a locally perturbed perfectly electrical conducting plate. Specific analysis is provided for the perfectly electrical conducting boundary condition and Maxwell's equations to accomplish the symmetric continuation, and a symmetric scattering problem with a bounded scatterer is obtained. To analyze the unique solvability and stability of time domain electromagnetic scattering problems, Fourier-Laplace transformation and a "Laplace domain to time domain" analysis are involved. A rigorous analysis implies the unique solvability and stability of the scattering problem with a locally perturbed plate and implies that the problem is equivalent to the symmetric scattering problem with a bounded scatterer.