几类二阶退缩型方程基本解的构造

The Construction of Elementary Solutions For Some Mixed Type Equations of Second Order

引言线性偏微分方程定性研究,是偏微分方程研究的重要方向之一。根据Hadamard以及后来我国学者一再重申的“所有线性偏微分方程的问题应该并且可以用基本解解决”的思想,研究线性各类方程基本解的构造,无疑有着重要的意义。

In this paper, we have constructed the elementary solutions of some linearpartial defferential equations of socond order, mainly by means of T which is the square ofthe geodesic distance between two points--the moving point ()and the fixed point (x_1, x_2,..., x_m) in the space of being the linear element ■These equations include the equations of the mixed type, the ultra--hyperbolic type and thetype which has some thing to do with the studing of the system of elliptic equation. There are many different methods to contruct the elementary solutions. But beginingwith T. it has very clear geometric significance and has very effective methods of construc-tion and calculation to construct the elementary solutions.