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Space-Time Discontinuous Galerkin Methods for Weak Solutions of Hyperbolic Linear Symmetric Friedrichs Systems
We study weak solutions and its approximation of hyperbolic linear symmetric Friedrichs systems describing acoustic, elastic, or electro-magnetic...
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An Algebraic Condition for the Exponential Stability of an Upwind Difference Scheme for Hyperbolic Systems
In the paper, we investigate the question of obtaining an algebraic condition for the exponential stability of the numerical solution of the upwind...
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High-Order ADER Discontinuous Galerkin Schemes for a Symmetric Hyperbolic Model of Compressible Barotropic Two-Fluid Flows
This paper presents a high-order discontinuous Galerkin (DG) finite-element method to solve the barotropic version of the conservative symmetric...
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On Critical Thresholds for Hyperbolic Balance Law Systems
We review the theoretical development in the study of critical thresholds for hyperbolic balance laws. The emphasis is on two classes of systems:...
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On the Quasilinearizability of Hyperbolic Monge–Ampère Systems
AbstractThe paper is devoted to establishing necessary and sufficient conditions for the local quasilinearizability of nondegenerate hyperbolic...
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Space-Time Solutions for Linear Hyperbolic Systems
The linear wave equation can be analyzed in the framework of symmetric Friedrichs systems as a special case of linear hyperbolic conservation laws....
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Fractional controllability of semilinear hyperbolic systems
This research considered the fractional controllability problem of internally controlled semilinear hyperbolic systems. In the first method, we show...
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A New Class of Simple, General and Efficient Finite Volume Schemes for Overdetermined Thermodynamically Compatible Hyperbolic Systems
In this paper, a new efficient, and at the same time, very simple and general class of thermodynamically compatible finite volume schemes is...
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Hyperbolicity and Rigidity for Fibred Partially Hyperbolic Systems
Every volume-preserving accessible centre-bunched fibred partially hyperbolic system with 2-dimensional centre either (a) has two distinct centre...
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Linear Quadratic Optimal Control for Systems Governed by First-Order Hyperbolic Partial Differential Equations
This paper focuses on linear-quadratic (LQ) optimal control for a class of systems governed by first-order hyperbolic partial differential equations...
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Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds
In this paper, a geometric process to compare solutions of symmetric hyperbolic systems on (possibly different) globally hyperbolic manifolds is...
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Maximally Symmetric Spaces
In this chapter we describe the geometry of maximally symmetric spaces such as spheres and the hyperbolic spaces in detail. We introduce different...
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Implicit-Explicit Bicompact Schemes for Hyperbolic Systems of Conservation Laws
AbstractHigh-order bicompact schemes for hyperbolic systems of conservation laws are considered. We aim to significantly speed up these schemes....
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A Discrete Analogue of the Lyapunov Function for Hyperbolic Systems
We study the difference splitting scheme for the numerical calculation of stable solutions of a two-dimensional linear hyperbolic system with...
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Entropy Stable Galerkin Methods with Suitable Quadrature Rules for Hyperbolic Systems with Random Inputs
In this paper, we investigate hyperbolic systems with random inputs based on generalized polynomial chaos (gPC) approximations, which is one of the...
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On Second-Order Parabolic and Hyperbolic Perturbations of a First-Order Hyperbolic System
AbstractWe study the Cauchy problems for a first-order symmetric hyperbolic system of equations with variable coefficients and its singular...
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Hyperbolic Conservation Laws
To describe and understand the full problem setting, we require some knowledge concerning hyperbolic conservation laws. In this section, we focus on...
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A Formal KAM Theorem for Hamiltonian Systems and Its Application to Hyperbolic Lower Dimensional Invariant Tori
In this paper we reformulate a formal KAM theorem for Hamiltonian systems with parameters under Bruno-Rüssmann condition. The proof is based on KAM...
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Volume growth and topological entropy of partially hyperbolic systems
Let f be a C 1 diffeomorphism on a compact manifold M admitting a partially hyperbolic splitting TM = E s ⊕≺ E 1 E 2 ⊕≺ ⋯ ⊕≺ E l ⊕≺ E u where E s is...