Poisson方程三类问题的通解  

General Solution of Three Problems for Poisson Equation

作　　者：郭时光[1,2] 

机构地区：[1]四川理工学院理学院,四川自贡643000 [2]人工智能四川省重点实验室,四川自贡643000

出　　处：《四川理工学院学报（自然科学版）》2014年第6期75-79,共5页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：人工智能四川省重点实验室开放基金项目(2012RYY04)

摘　　要：研究二维到四维空间上Poisson方程。采用求出其通解的方法,分别给出了该方程Cauchy问题、Direchlet问题和Neunmann问题的通解的解析表达式,从而得出其后面两类问题均存在无限多个解的结论。Researching the Poisson equations on 2 d to 4 d spaces. Through the method of finding out their general solu-tions, the analytic expressions of the general solutions of Cauehy problem, Direchlet problem and Neunmann problem for theequation are given respectively. Thus the conclusion that there are an unlimited number of solutions for the two behind typesof problems is obtained.

关 键 词：POISSON方程 Direchlet问题 Neunmann问题 推迟势 正规解 降维法 

分 类 号：O175.13[理学—数学]