一类EPD算子乘积与抛物算子乘积Cauchy问题解的结构关系

The Structure Relation of the Cauchy Problem Between the Producted Euler-Poisson-Darboux Operators and the Producted Parabolic Operator

1.引言 J.Hadamard首先研究了双曲方程与抛物方程基本解之间的关系,[3]建立了非抛物型方程Hadamard基本解的展开式系数升维洁构,并利用这种升维结构改进了[1]的结果;[5]解决了一类空间维数任意的双曲方程基本解、Cauchy问题解的极限问题。

In the case of coefficients are analytic, the elementary solution(In sense of Hadamard) and its dimension-accending structure, the relation between the elementary so- lutions, the Cauchy Problems for hyperbolic andparabolic equation had been studied wide- ly. Now, we deal with the structure relation between the singular Cauchy Problem of Prod- ucted Euler-Pisson-Darboux Operators with small parameter and the Cauchy Problem of Producted parabolic operators in any dimension p. We obtain the order-accending struc- ture of the elementary solution for the producted parabolic operators, especially. To be ex- act, We study the relation between the singular Cauchy Problem. and the cauchy problem there is a limited relation: lim s→0 u_s(t,x)=u(τ,χ);the order-accending styucture of the elementary solution for (* *) is where is the elementary solution of parabolic equation