Analysis of time‐domain elastic scattering by an unbounded structure

Abstract

This paper is devoted to the analysis of the time‐domain elastic wave scattering problem in an unbounded structure. The transparent boundary condition is developed to reformulate the scattering problem into an initial‐boundary value problem in an infinite slab. The well posedness and stability are established for the reduced problem in both the frequency and time domains. Our proofs are based on the energy method, the Lax‐Milgram theorem, and the inversion theorem of the Laplace transform. Moreover, a priori estimates with explicit dependence on the time are achieved for the elastic displacement by taking special test functions for the time‐domain variational problems of the Navier equation.