  We examine the transient scattered and transmitted fields generated when an
incident electromagnetic wave impinges on a dielectric scatterer or a coated
conductor embedded in an infinite space. By applying a boundary-field equation
method, we reformulate the problem in the Laplace domain using the electric
field equation inside the scatterer and a system of boundary integral equations
for the scattered electric field in free space. To analyze this nonlocal
boundary problem, we replace it by an equivalent boundary value problem.
Existence, uniqueness and stability of the weak solution to the equivalent BVP
are established in appropriate function spaces in terms of the Laplace
transformed variable. The stability bounds are translated into time-domain
estimates which determine the regularity of the solution in terms of the
regularity of the problem data. These estimates can be easily converted into
error estimates for a numerical discretization on the convolution quadrature
for time evolution.
