Related papers: Symmetric hyperbolic systems and shock waves
We discuss several topics related to the notion of strong hyperbolicity which are of interest in general relativity. After introducing the concept and showing its relevance we provide some covariant definitions of strong hyperbolicity. We…
Strongly correlated electron systems require the development of new theoretical schemes in order to describe their unusual and unexpected properties. The usual perturbation schemes are inadequate and new concepts must be introduced. In our…
At its core, hydrodynamics is a many-body low-energy effective theory for the long-wavelength, long-timescale dynamics of conserved charges in systems close to thermodynamic equilibrium. It has a wide range of applications spanning from…
We introduce novel approximate systems for dispersive and diffusive-dispersive equations with nonlinear fluxes. For purely dispersive equations, we construct a first-order, strictly hyperbolic approximation. Local well-posedness of smooth…
This article addresses linear hyperbolic partial differential equations with non-smooth coefficients and distributional data. Solutions are studied in the framework of Colombeau algebras of generalized functions. Its aim is to prove upper…
Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…
In classical continuum physics, a wave is a mechanical disturbance. Whether the disturbance is stationary or traveling and whether it is caused by the motion of atoms and molecules or the vibration of a lattice structure, a wave can be…
The main result of this work is the construction of multi-solitons solutions that is to say solutions that are time asymptotics to a sum of decoupling solitary waves for the full water waves system with surface tension.
We provide a consistent statistical-mechanical treatment for describing the thermodynamics and the structure of fluids embedded in the hyperbolic plane. In particular, we derive a generalization of the virial equation relating the bulk…
We derive a hyperbolic system of equations approximating the two-layer dispersive shallow water model for shear flows recently proposed by Gavrilyuk, Liapidevskii \& Chesnokov (J. Fluid Mech., vol. 808, 2016, pp. 441--468). The use of this…
Hyperbolic cross approximation is a special type of multivariate approximation. Recently, driven by applications in engineering, biology, medicine and other areas of science new challenging problems have appeared. The common feature of…
Lie symmetry analysis is applied to study the nonlinear rotating shallow water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow water equations are related…
The classical system of shallow-water (Saint--Venant) equations describes long surface waves in an inviscid incompressible fluid of a variable depth. Although shock waves are expected in this quasilinear hyperbolic system for a wide class…
We illustrate and emphasize the relevance of hyperbolic theories of dissipation in different physical scenarios. Particular attention is paid to self-gravitating systems where the relaxation time may become large enough as to require a…
We survey the theory of totally symmetric sets, with applications to homomorphisms of symmetric groups, braid groups, linear groups, and mapping class groups.
This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description…
The connection between several hyperbolic type metrics is studied in subdomains of the Euclidean space. In particular, a new metric is introduced and compared to the distance ratio metric.
The study of spherically symmetric motion is important for the theory of explosion waves. In this paper, we construct rigorously self-similar solutions to the Riemann problem of the spherically symmetric Euler equations for general…
After a short introduction to the characteristic geometry underlying weakly hyperbolic systems of partial differential equations we review the notion of symmetric hyperbolicity of first-order systems and that of regular hyperbolicity of…
The use of the hyperspherical harmonic (HH) basis in the description of bound states in an $A$-body system composed by identical particles is normally preceded by a symmetrization procedure in which the statistic of the system is taken into…