Arbitrariness of the general solution of the partial differential equations and its applications  

作　　者：Ding Qi Zhang HongQing 

机构地区：[1]Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

出　　处：《Science China Mathematics》2010年第7期1729-1739,共11页中国科学：数学（英文版）

基　　金：supported by the National Basic Research Program of China(Grant No. 2004CB318000);the "Math+X" Fund of Dalian University of Technology

摘　　要：Using the framework of formal theory of partial differential equations, we consider a method of computation of the bi-Hilbert polynomial (i.e. Hilbert polynomial in two variables). Furthermore, present an approach to compute the number of arbitrary functions of positive differential order in the general solution. Then, under the "AC=BD" model for mathematics mechanization developed by Hong-qing ZHANG, we present a method to reduce an overdetermined system to a well-determined one. As applications, the Maxwell equations and weakly overdetermined equations are considered.Using the framework of formal theory of partial differential equations, we consider a method of computation of the bi-Hilbert polynomial (i.e. Hilbert polynomial in two variables). Furthermore, present an approach to compute the number of arbitrary functions of positive differential order in the general solution. Then, under the 'AC=BD' model for mathematics mechanization developed by Hong-qing ZHANG, we present a method to reduce an overdetermined system to a well-determined one. As applications, the Maxwell equations and weakly overdetermined equations are considered.

关 键 词：'AC=BD' model INVOLUTION HILBERT POLYNOMIAL ARBITRARINESS overdetermined 

分 类 号：N[自然科学总论]