非水平分层区域Helmholtz边值问题的解析解

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The Analytical Solution for Helmholtz Boundary Problem in Non Horizontally Stratified Domains

摘要: 在(x,y,z)直角坐标系中,N个物性参数不同的区域D_j(j=0,1,…,N-1)充斥着整个空间,这些区域间的分界面是非水平的光滑曲面S_j,j+1下面的边值问题称为非水平分层区域Helmholtz边值问题:
∇²H^(j)+K_jH^(j)=0(j=0,1,…,N-1)
(H⁽⁰⁾-H⁽¹⁾)S_0.1=δ(S)(δ(S):广义δ-函数)
(H^(j)-H^(j+1))S_j,j+1=0(j=1,…,N-2)本文给出了此问题的解析解.

Abstract: There are N domains D_j(j=0,1,...,N-1) of different physical parameters in the whole space and their interfaces S_j,i+1 are non-horizontally smooth curved surfaces. The following boundary problem is called Hclinholiz boundary problem:
∇²H^(j)+K_jH^(j)=0 (j=0,1,…,N-1)
(H⁽⁰⁾-H⁽¹⁾)S_0.1=δ(S) (δ(S):generalized function)
(H⁽¹⁾-H⁽ⁱ⁺¹⁾)S_j,j+1=0 (j=0,1,…,N-2)
The analytical solution of the above problem is given in this paper.

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