一维热传导方程的绕射问题

THE DIFFRACTION PROBLEMS OF ONE-DIMENSIONAL HEAT FLOW EQUATION

本文分为两个部分,主要讨论了一维热传导方程的绕射问题。在第一部分解决无界区域上的绕射问题。首先,假定在间断处是一个已知的函数,然后求出解的表达式,再通过已知条件反求该函数的表达式,进而得到方程的解。是第二部分有界区域上的绕射问题,我们先利用对称开拓法,再通过一个巧妙的初等变换,把边界条件耦合在一起的方程分解成两个边界条件互相独立的方程分别求解。

Divided by two parts, this paper mainly discusses the diffraction problems of one - dimensional heat flow equations. We solve a equation on the unbounded district. We assume that there is a function that we have known in the interrupted. By doing this, we can find the espression type of the solution and get the espression type of the function by the conditions. Then we can slove the problem in the first part. While in the second part, by the symmetric estention and an ingenious elementary transformation, we separate the combined equation into two independent ones to solve.