超双曲型方程定性研究的几个问题

Some Problems of Qualitative Researches of the Ultra-hyperbolic Equation

本文主要提出起双曲型方程定性研究的几个问题:中量定理的推广与应用;广义势;解的延拓性;境界值问题。同时指出:Hadamard提出的“所有线性偏微分方程的问题,应该并且可以用基本解来解决”的思想,是开展超双曲型方程定性研究的途径。

The present paper is a resume in the qualitative researches of the ul- tra-hyperbolic equation, it involves the extensions of mean value theorem and its applications; the generilized potential; the continuations and bou- dary problems. Especially, we suggest to study the ultra-hyperbolic equn- ation by means of the elementary solution, which is a natual way.