Related papers: Equivalence of conservation laws and equivalence o…
We prove that potential conservation laws have characteristics depending only on local variables if and only if they are induced by local conservation laws. Therefore, characteristics of pure potential conservation laws have to essentially…
We construct a formally time-reversible, one-dimensional forced Burgers equation by imposing a global constraint of energy conservation, wherein the constant viscosity is modified to a fluctuating state-dependent dissipation coefficient.…
The equations of fluid motions are considered in the case of internal energy depending on mass density, volume entropy and their spatial derivatives. The model corresponds to domains with large density gradients in which the temperature is…
Thermodynamic systems involving reversible and non-reversible heat transfer are used to derive integral inequalities expected from the Second of Law of Thermodynamics. Then, the inequalities are proved and generalized to higher dimensions…
The Szekeres system is studied with two methods for the determination of conservation laws. Specifically we apply the theory of group invariant transformations and the method of singularity analysis. We show that the Szekeres system admits…
We report a new energy conservation law for time-harmonic electromagnetic fields, which is valid for an arbitrary medium. In contrast to the well-established Poynting theorem for time-harmonic fields, the real part of the new energy…
Isometric fluctuation relations are deduced for the fluctuations of the order parameter in equilibrium systems of condensed-matter physics with broken discrete or continuous symmetries. These relations are similar to their analogues…
We determine the Lie point symmetries of a Gardner type system and establish its nonlinear self-adjointness. We then construct conservation laws via Ibragimov's Theorem.
Interface dynamics in two-dimensional systems with a maximal number of conservation laws gives an accurate theoretical model for many physical processes, from the hydrodynamics of immiscible, viscous flows (zero surface-tension limit of…
Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories…
Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…
In this work we consider companion conservation laws to general systems of conservation laws. We investigate sufficient regularity for weak solutions to satisfy companion laws, assuming the fluxes to be $C^{1,\gamma}$, $0<\gamma<1$,…
The diagrammatic analysis of interacting particle assemblies harbors a fundamental mismatch between two of its main implementations: Phi-derivable (conserving) approximations and parquet (crossing symmetric) models. No termwise expansion,…
We consider entropy solutions to the initial value problem associated with scalar nonlinear hyperbolic conservation laws posed on the two-dimensional sphere. We propose a finite volume scheme which relies on a web-like mesh made of segments…
We show that, for first-order systems of conservation laws with a strictly convex entropy,in particular for the very simple so-called "inviscid" Burgers equation,it is possible to address the Cauchy problem by a suitable convex…
The interrelationship between energy and probability conservation is explored from the point of view of statistical physics and non-relativistic quantum mechanics. The simultaneous validity of the law of conservation of energy and the…
This article uses Cartan-K\"ahler theory to construct local conservation laws from covariantly closed vector valued differential forms, objects that can be given, for example, by harmonic maps between two Riemannian manifolds. We apply the…
The paper deals with perturbations of the equation that have a number of conservation laws. When a small term is added to the equation its conserved quantities usually decay at individual rates, a phenomenon known as a selective decay.…
Boltzmann's differential equation is replaced by the corresponding reciprocal symmetric finite difference equation. Finite difference translates discreteness of energy. Boltzmann's function, then, splits into two reciprocally related…
In this paper, we prove particle approximations of initial data for systems of conservation laws in two dimensions. This involves approaching the density but also all the additional quantities that could be verified by the model considered.…