线性齐次偏微分方程组吴特征列和Janet基的等价性

EQUALITY BETWEEN WU-CHARACTERISTIC SETS AND JANET BASES FOR LINEAR HOMOGENEOUS PARTIAL DIFFERENTIAL EQUATIONS

本文简单介绍了吴微分特征列和Janet基,利用线性齐次微分方程组既约化基的概念,证明了线性齐次偏微分方程组的正规化的吴微分特征列和正规化的、自约化的Janet基均是既约化基,从而由既约化基的唯一性,得到了它们的等价性定理。

First,Wu-characteristic sets and Janet bases for linear homogeneous partial differential equations（LHPDES） are introduced, and then using the concept of reduced bases for LHPDES, we draw a conclusion that both canonical Wu-characteristic set and canonical-autoreduced Janet bases for LHPDES are the reduced bases, and equality between them is obtained according to the uniqueness of the reduced bases.