A Naive Riemann Solver to Compute a Non-conservative Hyperbolic System

1999 ◽  
pp. 129-138
Author(s):  
Thierry Buffard ◽  
Thierry Gallouët ◽  
Jean-Marc Hérard
Keyword(s):  
Hyperbolic System ◽  
Riemann Solver

scholarly journals Diffeomorphism cocycles over partially hyperbolic systems

2020 ◽  
pp. 1-24
Author(s):  
VICTORIA SADOVSKAYA
Keyword(s):  
Hyperbolic System ◽  
Compact Manifold ◽  
Hyperbolic Systems ◽  
Riemannian Metrics ◽  
Hölder Continuous ◽  
Group Of Diffeomorphisms ◽  
Small Loss ◽  
Partially Hyperbolic ◽  
Loss Of Regularity

Abstract We consider Hölder continuous cocycles over an accessible partially hyperbolic system with values in the group of diffeomorphisms of a compact manifold $\mathcal {M}$ . We obtain several results for this setting. If a cocycle is bounded in $C^{1+\gamma }$ , we show that it has a continuous invariant family of $\gamma $ -Hölder Riemannian metrics on $\mathcal {M}$ . We establish continuity of a measurable conjugacy between two cocycles assuming bunching or existence of holonomies for both and pre-compactness in $C^0$ for one of them. We give conditions for existence of a continuous conjugacy between two cocycles in terms of their cycle weights. We also study the relation between the conjugacy and holonomies of the cocycles. Our results give arbitrarily small loss of regularity of the conjugacy along the fiber compared to that of the holonomies and of the cocycle.

Darboux problem for one hyperbolic system

2021 ◽  
Author(s):  
Lyubov B. Mironova
Keyword(s):  
Hyperbolic System ◽  
Darboux Problem

scholarly journals Characterization of Dissipative Structures for First-Order Symmetric Hyperbolic System with General Relaxation

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 728
Author(s):  
Yasunori Maekawa ◽  
Yoshihiro Ueda
Keyword(s):  
Hyperbolic System ◽  
Dissipative Structure ◽  
Dissipative Structures ◽  
Algebraic Characterization ◽  
Symmetric Hyperbolic System ◽  
Full Generality ◽  
Order Linear ◽  
First Order

In this paper, we study the dissipative structure of first-order linear symmetric hyperbolic system with general relaxation and provide the algebraic characterization for the uniform dissipativity up to order 1. Our result extends the classical Shizuta–Kawashima condition for the case of symmetric relaxation, with a full generality and optimality.

A study of higher-order reconstruction methods for genuinely two-dimensional Riemann solver

2021 ◽  
pp. 110469
Author(s):  
Boxiao Zhou ◽  
Feng Qu ◽  
Di Sun ◽  
Zirui Wang ◽  
Junqiang Bai
Keyword(s):  
Higher Order ◽  
Riemann Solver ◽  
Two Dimensional ◽  
Reconstruction Methods ◽  
Order Reconstruction
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