TIME-DOMAIN ANALYSIS OF FORWARD OBSTACLE SCATTERING FOR ELASTIC WAVE

This paper concerns a time-domain scattering problem of elastic plane wave by a rigid obstacle, which is immersed in an open space filled with homogeneous and isotropic elastic medium in two dimensions. A new compressed coordinate transformation is developed to reduce the scattering problem into an initial boundary value problem in a bounded domain over a finite time interval. The well-posednesss is established for the reduced problem. This paper adopts Galerkin method to prove the uniqueness results and employs energy method to derive stability results for the scattering problem. Furthermore, we achieve a priori estimate with explicit time dependence.