A Time-dependent Interaction Problem Between an Electromagnetic Field and an Elastic Body

This paper considers the scattering of a time-dependent electromagnetic plane wave by a bounded elastic body. An appropriate decomposition of the coupling interface conditions is proposed according to the Voigt’s model between the electromagnetic and elastic medium. The original unbounded scattering problem is equivalently reduced into an initial-boundary value problem in a bounded domain by introducing an exact transparent boundary condition (TBC) on a sufficiently large sphere. Making use of the Lax-Milgram lemma, the abstract inversion theorem of Laplace transform and the energy method, we verify the well-posedness and stability for the reduced problem. Moreover, a priori estimates are established for the electromagnetic field and elastic displacement by taking special test functions directly in the time domain variational formulation.