The method of boundary integral equations for a mixed scattering problem

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:246

Article

Yan, Guozheng¹  Yao, Mao¹ 

[1] Cent China Normal Univ, Dept Math & Appl Math, Wuhan 430079, Peoples R China

关键词: Helmholtz equation;    Boundary integral equation;    Existence and uniqueness;   

DOI  :  10.1016/j.jde.2009.02.012

来源: Elsevier

【 摘 要 】

In this paper we consider the scattering of an electromagnetic time-harmonic plane wave by an infinite cylinder having an open arc and a bounded domain in R-2 as cross section. To this end, we solve a scattering problem for the Helmholtz equation in R-2 where the scattering object is a combination of a crack Gamma and a bounded obstacle D, and we have Dirichlet-impedance type boundary condition on Gamma and Dirichlet boundary condition on partial derivative D (partial derivative D is an element of C-2). Applying potential theory, the problem can be reformulated as a boundary integral system. We establish the existence and uniqueness of a solution to the system by using the Fredholm theory. (c) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free