Darboux problem for one hyperbolic system

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

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.

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.

scholarly journals An inverse problem for a hyperbolic system on a vector bundle and energy measurements

2011 ◽  
Vol 354 (4) ◽  
pp. 1431-1464
Author(s):  
Katsiaryna Krupchyk ◽  
Matti Lassas
Keyword(s):  
Inverse Problem ◽  
Vector Bundle ◽  
Hyperbolic System

scholarly journals Local Exponential $H^2$ Stabilization of a $2\times2$ Quasilinear Hyperbolic System Using Backstepping

2013 ◽  
Vol 51 (3) ◽  
pp. 2005-2035 ◽  
Author(s):  
Jean-Michel Coron ◽  
Rafael Vazquez ◽  
Miroslav Krstic ◽  
Georges Bastin
Keyword(s):  
Hyperbolic System ◽  
Quasilinear Hyperbolic System

Kneser's theorem for weak solutions of the Darboux problem in Banach spaces

1993 ◽  
Vol 20 (2) ◽  
pp. 169-173 ◽  
Author(s):  
Dariusz Bugajewski ◽  
Staniśław Szufla
Keyword(s):  
Banach Spaces ◽  
Weak Solutions ◽  
Darboux Problem
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