一类重特征方程的Cauchy问题

A Class of Equations with Multiple Characteristics

本文引入变型算子．通过变型算子可以改变一类重特征方程的阶，因而变型算子成为研究这类重特征方程的有力工具．作为一个应用，导出了一个二阶重特征方程的非标准Ｃａｕｃｈｙ问题（只给一个初始数据）的解，证明了解的唯一性．

The type-changed operators are introduced in this paper. The order of a class of partial differential equations with multiple characteristics can be changed through the operators;therefor, such type-changed operators are powerful tools in studying some equations with multiple characteristics.As an example, the solution of the non-standard Cauchy problem (only one initial datum)for an equation of second order with multiple characteristics is gotten, and the uniqueness is proved.