常系数超双曲型方程解的明显公式

The Explicit Formula of Ultra-hyperbolic Equation with Constant Coefficient

一 引言 G.Homel在讨论几何学中直线为最短的问题时,考虑的方程等价于超双曲型方程:他证明了在二特征超平面邻近存在有函数满足方程,而在超平面上给出初值,但初值限制为对它三个变元中的两个是解杆的。Asgcirsson建立了超双曲型方程的中量定理。

In this paper, we use elementary solution and fundamental formula of ultra-hyperbolic equation to study ultra-hyperbolic equation with constant coefficient and have results: If u is a regular solution of ultra-hyperbolic equation with constant coefficient the variable vary in a domain by an initial hypersuface and the characteristic conoid, an integral formula is derived that gives the value of the solution u at the vertex of this conoid and necessary condition for the initial value is derived.