相关论文: Lyapunov Functionals for the Enskog Equation
Energy (or Lyapunov) functions are used to prove stability of equilibria, or to indicate a gradient-like structure of a dynamical system. Matano constructed a Lyapunov function for quasilinear non-degenerate parabolic equations. We modify…
In this paper, we study a new type of stochastic functional differential equations which is called hybrid pantograph stochastic functional differential equations. We investigate several moment properties and sample properties of the…
This article introduces a conservative formulation of the Standard Enskog equation and the Povzner equation, both of which generalize the Boltzmann equation by incorporating the contribution of particle volume in collisions. The primary…
Two dimensional quantum R$^2$-gravity and its phase structure are examined in the semiclassical approach and compared with the results of the numerical simulation. Three phases are succinctly characterized by the effective action. A…
For systems evolving on a Riemannian manifold, we propose converse Lyapunov theorems for asymptotic and exponential stability. The novelty of the proposed approach is that is does not rely on local Euclidean coordinate, and is thus valid on…
The Lagrangian formulation of classical mechanics is widely applicable in solving a vast array of physics problems encountered in the undergraduate and graduate physics curriculum. Unfortunately, many treatments of the topic lack…
We give a survey of classical and recent results on sharp constants and symmetry/asymmetry of extremal functions in $1$-dimensional functional inequalities.
We show that considering time measured by an observer to be a function of a cyclical field (an abstract version of a clock) is consistent with Hamilton's and Lagrange's equations of motion for a one dimensional space manifold. The…
We show that it is possible to obtain self-consistent and physically acceptable relativistic classical equations of motion for a point-like spin-half particle possessing an electric charge and a magnetic dipole moment, directly from a…
From the analyticity properties of the equation governing infinitesimal perturbations, it is shown that all stability properties of spatially extended 1D systems can be derived from a single function that we call entropy potential since it…
New, gauge-independent, second-order Lagrangian for the motion of classical, charged test particles is proposed. It differs from the standard, gauge-dependent, first order Lagrangian by boundary terms only. A new method of deriving…
We report the statistical properties of classical particles in (2+1) gravity as resulting from numerical simulations. Only particle momenta have been taken into account. In the range of total momentum where thermal equilibrium is reached,…
We discuss the form of the entropy for classical hamiltonian systems with long-range interaction using the Vlasov equation which describes the dynamics of a $N$-particle in the limit $N\to\infty$. The stationary states of the hamiltonian…
Using the symplectic tomography map, both for the probability distributions in classical phase space and for the Wigner functions of its quantum counterpart, we discuss a notion of Lyapunov exponent for quantum dynamics. Because the…
A Path-Complete Lyapunov Function is an algebraic criterion composed of a finite number of functions, called its pieces, and a directed, labeled graph defining Lyapunov inequalities between these pieces. It provides a stability certificate…
For an integral functional defined on functions $(u,v)\in W^{1,1}\times L^1$ featuring a prototypical strong interaction term between $u$ and $v$, we calculate its relaxation in the space of functions with bounded variations and Radon…
The Vlasov-Poisson equation is a classical example of an effective equation which shall describe the coarse-grained time evolution of a system consisting of a large number of particles which interact by Coulomb or Newton's gravitational…
This paper considers the stability problem of a linear time invariant system in feedback with a string equation. A new Lyapunov functional candidate is proposed based on the use of augmented states which enriches and encompasses the…
Solutions of a smooth first order dynamic equation can be made Lyapunov stable at will by the choice of an appropriate time-dependent Riemannian metric.
An approach for computing Lyapunov functions for nonlinear continuous-time differential equations is developed via a new, Massera-type construction. This construction is enabled by imposing a finite-time criterion on the integrated…