热传导方程解的梯度估计和解析性  

Gradient Estimation and Analytic Properties of Solutions to Heat Conduction Equations

作　　者：邢家省[1,2] 杨义川[1,2] 吴桑 XING Jiasheng;YANG Yichuan;WU Sang(School of Mathematics and Systems Science, Beihang University, Beijing 100191, China;LMIB of the Ministry of Education, Beihang University, Beijing 100191, China)

机构地区：[1]北京航空航天大学数学科学学院,北京100191 [2]数学、信息与行为教育部重点实验室,北京100191

出　　处：《吉首大学学报（自然科学版）》2020年第4期6-11,共6页Journal of Jishou University(Natural Sciences Edition)

基　　金：国家自然科学基金资助项目(11771004);北京航空航天大学校级重大教改项目(北航培育项目201901—202112)。

摘　　要：利用热传导方程初值问题的求解公式,给出了齐次热传导方程初值问题的解是解析函数的证明.对齐次热传导方程的解给出了梯度估计,并通过对各阶偏导数的估计应用泰勒公式,给出了齐次热传导方程的解是解析函数的证明.This paper provesthat the solution of the initial value problem for homogeneous heat conduction equation is an analytical function by the solution formula of the initial value problem for the heat conduction equation.The paper provides the gradient estimation of solutions for homogeneous heat conduction equation,offers the method of proving that the solution of homogeneous heat conduction equation is an analytical function by estimating the partial derivative of each order and applying Taylor formula.

关 键 词：热传导方程 热传导方程解 初值问题 梯度估计 解析函数 

分 类 号：O175.29[理学—数学]