【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.更多还原

【Abstract】 This paper discusses the Dirichlet-Neumann-Third boundary value problem of Helmholtz equation in scattering theory:△u+k²u=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 R³,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.更多还原