时域弹性波在周期结构中的散射问题

Time domain scattering for elastic waves in a biperiodic structure

本文研究时域弹性波在双周期结构中的散射问题.针对无界区域中三维时域Navier方程,本文提出利用压缩坐标变换的方法将散射问题转化为有限时间区间上的初边界值问题,然后采用Galerkin方法证明此散射问题弱解的唯一性,并利用能量分析方法对解建立稳定性估计和具有显式时间依赖性的先验估计.

This paper concerns the mathematical analysis of the scattering of an elastic plane wave by a biperiodic structure.The wave propagation is governed by the time-domain Navier equation in three dimensions.The method of a compressed coordinate transformation is developed to reduce equivalently the scattering problem into an initial-boundary value problem formulated in a bounded domain over a finite time interval.The reduced problem is shown to have a unique weak solution by using the constructive Galerkin method.The stability and a priori estimates with explicit time dependence are established for the weak solution.