Systems of hyperbolic conservation laws with prescribed eigencurves
Systems of hyperbolic conservation laws with prescribed eigencurves
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具有规定特征曲线的双曲守恒定律系统
DOI：
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发表时间：
2009
期刊：
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通讯作者：
I. Kogan
中科院分区：
文献类型：
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作者：
H. Jenssen;I. Kogan
本文研究了一维双曲守恒律方程组的构造问题，给出了方程组的特征曲线，即给出了通量雅可比矩阵的特征向量场。我们制定这作为一个典型的超定系统的方程的特征值。被认为是在微分和代数微分方程的等效配方。然后使用适当的可积性定理（Frobenius，Darboux和Cartan-Kahler）分析所得方程。我们给出了一个完整的分析可能的情况下，包括例子，系统的三个方程。作为一个应用，我们描述保守系统具有相同的特征曲线的欧拉系统的1维可压缩气体动力学。任何规模的一般丰富系统的情况下（即当给定的特征向量场成对对合时;这包括所有两个方程的系统）是完全解决的，我们考虑这类中的各种例子。
We study the problem of constructing systems of hyperbolic conservation laws in one space dimension with prescribed eigencurves, i.e. the eigenvector fields of the Jacobian of the flux are given. We formulate this as a typically overdetermined system of equations for the eigenvalues-to-be. Equivalent formulations in terms of differential and algebraic-differential equations are considered. The resulting equations are then analyzed using appropriate integrability theorems (Frobenius, Darboux and Cartan-Kahler). We give a complete analysis of the possible scenarios, including examples, for systems of three equations. As an application we characterize conservative systems with the same eigencurves as the Euler system for 1-dimensional compressible gas dynamics. The case of general rich systems of any size (i.e. when the given eigenvector fields are pairwise in involution; this includes all systems of two equations) is completely resolved and we consider various examples in this class.