摘要
根据解析函数和线性算子的基本性质定义了一类线性算子，建立了关于这种算子的完整理论，然后把一般形式的高阶常系数线性偏微分方程初值问题的解析解用这种算子表示出来；通过把这种算子表示成积分形式，这种算子形式的偏微分方程解就转化为积分形式的解，我们就彻底解决了把任意阶常系数线性偏微分方程初值问题的解析解求出并表示成给定函数的积分这一重要课题。
OPERATORS TO PARTIAL DIFFERENTIAL EQUATIONS $$$$ Bi Guangqing (No.2 Middle school of Yanan , Yanan 716000) Abstract Based on the basic properties of analytic functions and linear operators a class of linear operators is defined and a systematic theory of it is established. Further, all the analytic solutions to an initial value problem of an arbetrary order linear partial differental equation are expressed in these linear operators. By writing operators in this class into integral forms, the solutions in operator form are represented into integral forms. We thus solved the important problem of trpresenting the solutions of partial differential equations of any order into the integrations of some given functions without traditional classification or other analysis.
出处
《纯粹数学与应用数学》
CSCD
1997年第1期7-14,共8页
Pure and Applied Mathematics
关键词
抽象算子
解析函数
偏微分方程
解析解
abstract operators
analytic functions
linear partial differential equations
analytic solutions
