散射理论中多连通域的混合边值问题  

The Boundary Value Problem of the Multiple Connected Domain in Scattering Theory

作　　者：张万国[1] 

机构地区：[1]复旦大学数学系,200433

出　　处：《应用数学》1991年第1期38-45,共8页Mathematica Applicata

基　　金：国家自然科学基金;上海自然科学基金

摘　　要：本文讨论了散射理论中的Helmholtz方程在多连通域中的Dirichlet-Neumann-第三混合边值问题.文章建立了与此边值问题对应的积分方程组,并讨论了此问题解的性质及对应的积分方程零空间的性质.This paper discusses the Dirichlet-Neumann-Third boundary value problem of Helmholtz equation in scattering theory:△u+k^2u=0,x∈Ω,u=f(x),x∈S_D,((?)u)/((?)n)=-h(x)u+g,x∈S_(NT), wher eu(x) is an unknown complex function, Ω is a multiply connected domain in R^3,S_d and S_(nt) are the subsets of the boundary of Ω, which are nonempty sets and each of which is decomposable into a finite number of disjoint closed Lyapunov surfaces, f(x) and g(x) are continuous functions, h(x)≥0. We get an equivalent system of two integral equations of the second kind. The behaviour of the solution of this problem and the null space of integral equations are also discussed.

关 键 词：H-方程 积分方程组 边值 散射理论 

分 类 号：O175.8[理学—数学]