相关论文: Theory and applications of the Vlasov equation

This paper outlines a variety of possible applications of the Vlasov equation and its generalization, i.e., the Klimontovich equation, in various areas of many-body physics. In particular, these equations are shown to be used in…

In this editorial survey we introduce the special issue of the journal Communications in Mathematics on the topic in the title of the article. Our main goal is to briefly outline some of the main aspects of this important area at the…

The goal of this Section is to formulate some of the basic results on the theory of integral equations and mention some of its applications. The literature of this subject is very large. Proofs are not given due to the space restriction.…

This paper revises traditional phenomenological approaches to the application of Vlasov equation to describe the dissipative systems. The original equation by A.A. Vlasov obtained differs from the classical Vlasov equation used in the…

We present Vlasov's equation and its association with Poisson's equation in the context of modelling self-gravitating systems such as Globular Clusters or Galaxies. We first review the classical hypotheses of the model. We continue with a…

We analyse a reduced 1D Vlasov--Maxwell system introduced recently in the physical literature for studying laser-plasma interaction. This system can be seen as a standard Vlasov equation in which the field is split in two terms: an…

In this paper, we present very first results for the adaptive solution on a grid of the phase space of the Vlasov equation arising in particles accelarator and plasma physics. The numerical algorithm is based on a semi-Lagrangian method…

The method of obtaining of Vlasov-type equations for systems of interacting massive charged particles from the general relativistic Einstein-Hilbert action is considered. An effective approach to synchronizing the proper times of various…

A stochastic representation for the solutions of the Poisson-Vlasov equation is obtained. The representation involves both an exponential and a branching process. The stochastic representation, besides providing an alternative existence…

These are lecture notes on the subject defined in the title. As such, they do not pretend to be really new, probably except for the only section about Poisson equations with potentials. Yet, the hope of the author is that they may serve as…

In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…

In this paper, we are interested in a generalised Vlasov equation, which describes the evolution of the probability density of a particle evolving according to a generalised Vlasov dynamic. The achievement of the paper is twofold. Firstly,…

The purpose of this paper is to study the relations between different concepts of dispersive solution for the Vlasov-Poisson system in the gravitational case. Moreover we give necessary conditions for the existence of partially and totally…

A hybrid model of the Vlasov equation in multiple spatial dimension $D>1$ [H. A. Rose and W. Daughton, Physics of Plasmas v. 18, 122109 (2011)], the Vlasov multi dimensional model (VMD), consists of standard Vlasov dynamics along a…

A stochastic representation for the solutions of the Poisson-Vlasov equation, with several charged species, is obtained. The representation involves both an exponential and a branching process and it provides an intuitive characterization…

Relativistic dissipative fluid dynamics finds widespread applications in high-energy nuclear physics and astrophysics. However, formulating a causal and stable theory of relativistic dissipative fluid dynamics is far from trivial; efforts…

Particle-based simulations of the Vlasov equation typically require a large number of particles, which leads to a high-dimensional system of ordinary differential equations. Solving such systems is computationally very expensive, especially…

A new modified Vlasov equation has been obtained in this paper for the systems with dissipative phenomena such as, for example, plasma with irradiation.

Partial differential equations (PDEs) are at the heart of many mathematical and scientific advances. While great progress has been made on the theory of PDEs of standard types during the last eight decades, the analysis of nonlinear PDEs of…

When the Vlasov equation is investigated numerically using the method of test particles, the particle-particle interactions that inevitably arise in the simulation (but are not present in the Vlasov equation itself) result in an…