Elastic scattering from rough surfaces in three dimensions

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Hu, Guanghui¹  Li, Peijun²  Zhao, Yue³ 

[1] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[3] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China

关键词: Elastic wave equation;    Rigid rough surface;    Variational method;    Local perturbation;    Green's tensor;    Radiation condition;   

DOI  :  10.1016/j.jde.2020.03.022

来源: Elsevier

【 摘 要 】

Consider the elastic scattering of a plane or point incident wave by an unbounded and rigid rough surface. The angular spectrum representation (ASR) for the time-harmonic Navier equation is derived in three dimensions. The ASR is utilized as a radiation condition to the elastic rough surface scattering problem. The uniqueness is proved through a Rellich-type identity for surfaces given by uniformly Lipschitz functions. In the case of flat surfaces with local perturbations, an equivalent variational formulation is deduced in a truncated bounded domain and the existence of solutions are shown for general incoming waves. The main ingredient of the proof is the radiating behavior of the Green tensor to the first boundary value problem of the Navier equation in a half-space. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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