2016/08/19 by Yixian Gao, Gao, Yixian, Peijun Li +3 · 1 citation
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1608.05647
openalex publication_date 2016/08/19 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
Consider the wave propagation in a two-layered medium consisting of a homogeneous compressible air or fluid on top of a homogeneous isotropic elastic solid. The interface between the two layers is assumed to be an unbounded rough surface. This paper concerns the time-domain analysis of such an acoustic-elastic interaction problem in an unbounded structure in three dimensions. Using an exact transparent boundary condition and suitable interface conditions, we study an initial-boundary value problem for the coupling of the Helmholtz equation and the Navier equation. The well-posedness and stability are established for the reduced problem. Our proof is based on the method of energy, the Lax--Milgram lemma, and the inversion theorem of the Laplace transform. Moreover, a priori estimates with explicit dependence on the time are achieved for the quantities of acoustic pressure and elastic displacement by taking special test functions for the time-domain variational problem.