Variational Approach to Scattering by Inhomogeneous Layers Above Rough Surfaces

作     者：LUAN TIAN MA FU-MING 

作者机构：College of MathematicsJilin University College of MathematicsBeihua University 

出 版 物：《Communications in Mathematical Research》 (数学研究通讯（英文版）)

年 卷 期：2014年第30卷第1期

页      面：71-80页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：The Education Department.(12531136) of Heilongjiang the NSF(10971083,51178001) of China Science and Technology Research Project.(2014213) of Jilin Province Department of Education 

主　　题：Helmholtz equation rough surface scattering problem 

摘      要：In this paper, we study, via variational methods, the problem of scattering of time harmonic acoustic waves by unbounded inhomogeneous layers above a sound soft rough surface. We first propose a variational formulation and exploit it as a theoretical tool to prove the well-posedness of this problem when the media is non-absorbing for arbitrary wave number and obtain an estimate about the solution, which exhibit explicitly dependence of bound on the wave number and on the geometry of the domain. Then, based on the non-absorbing results, we show that the variational problem remains uniquely solvable when the layer is absorbing by means of a priori estimate of the solution. Finally, we consider the finite element approximation of the problem and give an error estimate.