Method of characteristics and first integrals for systems of quasi-linear partial differential equations of first order

被引：3

作者：

Han, ChongKyu ^{[1
]}

Park, JongDo ^{[2
,3
]}

机构：

[1] Seoul Natl Univ, Dept Math, Seoul 151742, South Korea

[2] Kyung Hee Univ, Dept Math, Seoul 130701, South Korea

[3] Kyung Hee Univ, Res Inst Basic Sci, Seoul 130701, South Korea

来源：

SCIENCE CHINA-MATHEMATICS | 2015年 / 58卷 / 08期

基金：

新加坡国家研究基金会;

关键词：

overdetermined PDE system; quasi-linear first order PDEs; first integrals; Pfaffian systems; Frobenius theorem; RIEMANN INVARIANTS; PFAFFIAN SYSTEMS; HYPERBOLIC SYSTEMS; WAVES;

D O I：

10.1007/s11425-014-4942-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a set of independent vector fields on a smooth manifold, we discuss how to find a function whose zero-level set is invariant under the flows of the vector fields. As an application, we study the solvability of overdetermined partial differential equations: Given a system of quasi-linear PDEs of first order for one unknown function we find a necessary and sufficient condition for the existence of solutions in terms of the second jet of the coefficients. This generalizes to certain quasi-linear systems of first order for several unknown functions.

引用

页码：1665 / 1676

页数：12

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