Tricomi算子的基本解

The Fundamental Solution for the Tricomi Operator

考虑含三个自变量的Tricomi方程Tu=y(u_(x_1x_1)+u_(x_2x_2))+u_(yy)=0 (1)奇点为(a,b,0)的基本解.相对于两维的Tricomi方程,由于其奇性的增强,用通常的分布论计算基本解时,得到的积分发散,以致无法用该方法得到基本解,此时有必要引入散度积分主部来定义分布论中的基本解.我们利用特征线法在Cauchy主值意义下求得其基本解.

We give the fundamental solution of the Tricomi operator Tu=y（ux1x1＋ux2x2）＋uyy=0 （I It has stronger singularity than Tu = yuxx ＋ Uyy =. 0. We indicate that it is necessary to introduce the principal part of Cauchy integral to define the fundamental solution in the theory of distribution.