scholarly journals Viscous shock profile and singular limit for hyperbolic systems with Cattaneo's law

2018 ◽  
Vol 11 (4) ◽  
pp. 795-819 ◽  
Author(s):  
Tohru Nakamura ◽  
◽  
Shuichi Kawashima ◽  
Keyword(s):  
Hyperbolic Systems ◽  
Singular Limit ◽  
Shock Profile ◽  
Cattaneo’S Law

Control of Pseudo-Hyperbolic Systems by Concentrated Impacts

2000 ◽  
Vol 32 (12) ◽  
pp. 23-36 ◽  
Author(s):  
Sergey I. Lyashko ◽  
Vladimir V. Semenov ◽  
Ivan I. Lyashko
Keyword(s):  
Hyperbolic Systems

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.

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