热传导方程Cauchy问题某些特殊情形的简便算法

A HANDY SOLUTION OF SOME SPECIAL CASES OF CAUCHY PROBLEM OF THE HEAT CONDUCTION EQUATION

一般热传导方程柯西（Ｃａｕｃｈｙ）问题的解由满足初始条件的函数的积分来表示，即使较简单，要计算出这些复杂的广义积分也不是一件易事。本文提供了一种算法，对某些初始条件，只需计算其高阶拉普拉斯算子，就可以得到方程的显解。计算较简捷，解的形式统一，结构简单，其方法适用于满足一定条件的有限维热传导方程的柯西问题。

In this paper,we provide a handy method of solving certain Cauchy problem of the heat conduction equation.For certain initial conditions,we need only calculate their high order Laplace operator,then we can obtain the accurate solution of the initial value problem.This method is easier than the normally adopted one,the solution has uniform expression and the construction of the solution is simple.This method is suitable to finite dimensional Cauchy problem of heat conduction equation satisfying certain condition.