热传导方程的基本解与正态分布密度函数  

Discussion of the elementary solution to heat equation and density fuction of normal distribution

作　　者：刘转转[1] 刘茂省[1] 张菊萍[1] 

机构地区：[1]中北大学理学院数学系,山西太原030051

出　　处：《西南民族大学学报（自然科学版）》2012年第2期170-173,共4页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10901145);山西省青年基金(2011021001-2)

摘　　要：基于热传导方程的基本解是正态分布的密度函数,一方面从概率角度利用正态分布的密度函数的性质对热传导方程解的性质进行了分析,另一方面借助于热传导方程初值问题解的两种不同形式得到了一类期望的级数算法.The elementary solution to Cauchy problem of heat equation is the density function of normal distri-bution.According to this,on the one hand,the characteristics of solution to heat equation are explained by density function of normal distribution.On the other hand because of the uniqueness of the solution to Cauchy problem of heat equation,a class of mathematical expectation can be changed into progression with differential operator.

关 键 词：热传导方程 基本解 正态分布 数学期望 级数 

分 类 号：O21[理学—概率论与数理统计]