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