一类偏微分方程定解问题的古典解

The Classical Solution of A Class of definite Solution Problem of Partial Differential Equations

研究热传导方程带有周期条件的定解问题,根据分离变量法把PDE问题转化为积分方程问题,然后利用逐次逼近法和压缩映射原理证明积分方程问题解的存在唯一性,最后证明该积分方程的解就是原PDE问题的古典解.

In this paper,we study the definite solution problem of heat equation with periodic conditions.We firstly transform this partial differential equation into an integral equation with the method of separation of variables,then using the methods of successive approximation and contraction mapping principle to prove the existence and uniqueness of the solution of this integral equation problem,and finally we can prove that the solution of this integral equation problem is exactly the classical solution of the original partial differential equation problem.