SYSTEMS OF HYPERBOLIC CONSERVATION LAWS WITH PRESCRIBED EIGENCURVES

Author:

JENSSEN HELGE KRISTIAN1,KOGAN IRINA A.2

Affiliation:

1. Department of Mathematics, Penn State University, State College, Pennsylvania 16802, USA

2. Department of Mathematics, North Carolina State University, Raleigh, North Carolina, 27695, USA

Abstract

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–Kähler). 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics,Analysis

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Jacobians with prescribed eigenvectors;Differential Geometry and its Applications;2019-08

2. NONUNIQUENESS OF BV SOLUTIONS OF QUASILINEAR HYPERBOLIC SYSTEMS;Journal of Hyperbolic Differential Equations;2012-12

3. Extensions for Systems of Conservation Laws;Communications in Partial Differential Equations;2012-03-30

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