论抛物型方程初—边值问题和初值问题解法的统一性

ON UNITY OF THE SOLUTION TO PARABOLIC TYPE INITIAL—BOUNDARY VALUE PROBLEM AND INITIAL VALUE PROBLEM

本文尝试将抛物型方程初—边值问题中的初始函数在相应的本征函数族下展开成为 Fourier 级数,把初始函数延拓到整个数轴,把初—边值问题转化成为初值问题,从而使这两类不同的定解问题的解法统一起来。

In this paper,the initial function among initial-boundary value problem for heat equations is expanded to a Fourier series under relevant eigenfunction system and the solu- tion of the initial-boundary value problem is redueed to initial value problem by the con- tinuation of the initial function outside the given interval.The integration of these two dif- ferent methods is madc.