【摘要】 考虑一类扩充的非齐次超双曲型方程: (其中c为任意实常数) 本文在乘积空间的有界闭单联域上,再次建立了广义的Asgeirsson中量及推广Asgeirsson公式。我们的结果还包含了著名数学家Hans.Lewy的一个结果。从而把众所周知的Huyghens原理扩充到这类超双曲型方程。本文的方法,是在引入广义Asgeirsson球面中量后,导出其所适合的微分方程,在不同角域中提出两类含两根奇线的Cauchy问题,通过使用1969年E.C.Young(杨格)的结果及借助Riemann(黎曼)方法予以求解,最后经过衔接得到中量定理,等等。并解释了在一类特征流型上的Huyghens原理。更多还原

【Abstract】 The purpose of this paper is to establish a generalized Asgeirsson’s theorem of spherical averages for the nonhomogeneous ultrahyperbolic equation. The answer is affirmative and this is proved in what follows, together with a generalization of Asgeirsson’s formula to the nonhomogeneous ultrahyperbolic equation. Therefore, this paper obtains the extension of Huyghens principle to nonhomogeneous ultrahyperbolic equation on a certain characteristic manifold. The importance of the Asgeirsson mean value theorem is well known, the result of this paper is the extension of this theorem: The methods taken here are the Riemann’s method and that by means of the solution of singular Cauchy problems更多还原