%0 Journal Article
%T N-DIMENSIONAL MULTIPLE NON-HOMOGENEOUS HARMONIC EQUATION AND ITS BOUNDARY INTEGRAL EQUATION<br>N维多重非齐次调和方程及其边界积分方程
%A TAN Junyu
%A ZHANG Linhua
%A WU Yong
%A <br>谈骏渝
%A 张林华
%A 吴永
%J 系统科学与数学
%D 2010
%I 
%X In this paper, the $n$-dimensional multiple non-homogeneous harmonic equation ${\it \Delta}^{(k)}u=f(x),x\in\mbox{\boldmath $R$}^{n}$, is considered. Firstly, the fundamental solution and its recurrence formulae are given. Then some fundamental integral relations are presented, specially, for multiple harmonic function. Under the assumption that non-homogeneous term $f(x)$ is $m$-degree harmonic, the integral term in domain is shifted boundary integral, and hence the boundary integral equation without integral in domain is obtained. Finally, the error and convergence analysis is discussed by Taylor polynomial approximation of non-homogeneous term $f(x)$.
%K Multiple harmonic equation
%K boundary integral equation
%K fundamental solution
%K k-degree harmonic function
%K weak solution<br>多重调和方程
%K 边界积分方程
%K 基本解
%K $k$-次调和函数
%K 弱解.
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=0DE0F7F8DFE70B9EA969F1C82637FCA8&yid=140ECF96957D60B2&vid=340AC2BF8E7AB4FD&iid=E158A972A605785F&sid=D9202C57BAB9096F&eid=98494933359B55EC&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=0&reference_num=13