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The Vlasov-Maxwell-Boltzmann system is a fundamental model to describe the dynamics of dilute charged particles, where particles interact via collisions and through their self-consistent electromagnetic field. We prove the existence of…

Analysis of PDEs · Mathematics 2010-05-02 Robert M. Strain

The Vlasov-Poisson-Boltzmann system is often used to govern the motion of plasmas consisting of electrons and ions with disparate masses when collisions of charged particles are described by the two-component Boltzmann collision operator.…

Analysis of PDEs · Mathematics 2017-10-25 Renjun Duan , Shuangqian Liu

An important physical model describing the dynamics of dilute weakly ionized plasmas in the collisional kinetic theory is the Vlasov-Poisson-Boltzmann system for which the plasma responds strongly to the self-consistent electrostatic force.…

Analysis of PDEs · Mathematics 2012-03-20 Renjun Duan , Tong Yang , Huijiang Zhao

In this paper we discuss the dissipative property of near-equilibrium classical solutions to the Cauchy problem of the Vlasov-Maxwell-Boltzmann System in the whole space $\R^3$ when the positive charged ion flow provides a spatially uniform…

Analysis of PDEs · Mathematics 2011-07-12 Renjun Duan

We investigate the long time behavior of a system of viscoelastic particles modeled with the homogeneous Boltzmann equation. We prove the existence of a universal Maxwellian intermediate asymptotic state and explicit the rate of convergence…

Analysis of PDEs · Mathematics 2015-06-16 Ricardo J. Alonso , Bertrand Lods

When dilute charged particles are confined in a bounded domain, boundary effects are crucial in the global dynamics. We construct a unique global-in-time solution to the Vlasov-Poisson-Boltzmann system in convex domains with the diffuse…

Analysis of PDEs · Mathematics 2019-04-08 Yunbai Cao , Chanwoo Kim , Donghyun Lee

This review is a kinetic theory study investigating the effects of inelasticity on the structure of the non-equilibrium states, in particular on the behavior of the velocity distribution in the high energy tails. Starting point is the…

Statistical Mechanics · Physics 2007-05-23 R. Brito , M. H. Ernst

Since the work [13] by Guo [Invent. Math. 153 (2003), no. 3, 593--630], how to establish the global existence of perturbative classical solutions around a global Maxwellian to the Vlasov-Maxwell-Boltzmann system with the whole range of soft…

Analysis of PDEs · Mathematics 2014-11-20 Renjun Duan , Yuanjie Lei , Tong Yang , Huijiang Zhao

In this paper we study the Hamiltonian dynamics of charged particles subject to a non-self-consistent stochastic electric field, when the plasma is in the so-called weak turbulent regime. We show that the asymptotic limit of the Vlasov…

Analysis of PDEs · Mathematics 2021-10-13 Claude Bardos , Nicolas Besse

The dynamics of dilute electrons can be modeled by the fundamental one-species Vlasov-Poisson-Boltzmann system which describes mutual interactions of the electrons through collisions in the self-consistent electrostatic field. For cutoff…

Analysis of PDEs · Mathematics 2015-06-19 Qinghua Xiao , Linjie Xiong , Huijiang Zhao

Dynamics of inelastic gases are studied within the framework of random collision processes. The corresponding Boltzmann equation with uniform collision rates is solved analytically for gases, impurities, and mixtures. Generally, the energy…

Statistical Mechanics · Physics 2007-05-23 E. Ben-Naim , P. L. Krapivsky

The spatially homogeneous Vlasov-Nordstr\"{o}m-Fokker-Planck system is known to exhibit nontrivial large time behavior, naturally leading to weak diffusion of the Fokker-Planck operator. This weak diffusion, combined with the singularity of…

Analysis of PDEs · Mathematics 2024-09-10 Shengchuang Chang , Shuangqian Liu , Tong Yang

The Boltzmann equation is essential for gas thermodynamics,as it models how the molecular density distribution $F(t,x,v)$ changes over time. However, existing research primarily focuses on the single species Boltzmann equation, while…

Analysis of PDEs · Mathematics 2026-01-30 Gaofeng Wang , Weike Wang , Tianfang Wu

We study the permanent regimes of the reduced Vlasov-Maxwell system for laser-plasma interaction. A non-relativistic and two different relativistic models are investigated. We prove the existence of solutions where the distribution function…

Analysis of PDEs · Mathematics 2009-11-11 Mihai Bostan , Simon Labrunie

The velocity distribution of inelastic granular gas is examined numerically on two dimensional hard disk system in nearly elastic regime using molecular dynamical simulations. The system is prepared initially in the equilibrium state with…

Statistical Mechanics · Physics 2009-11-07 Hiizu Nakanishi

The dynamics of dilute plasma particles such as electrons and ions can be modeled by the fundamental two species Vlasov-Poisson-Boltzmann equations, which describes mutual interactions of plasma particles through collisions in the…

Analysis of PDEs · Mathematics 2025-04-01 Zaihong Jiang , Yong Wang , Hang Xiong

In this paper, we study the Vlasov-Maxwell-Boltzmann system without angular cutoff and the Vlasov-Maxwell-Landau/Boltzmann system with polynomial perturbation $F=\mu+f$ near global Maxwellian. In particular, we prove the global existence,…

Analysis of PDEs · Mathematics 2023-12-27 Chuqi Cao , Dingqun Deng , Xingyu Li

The motion of a collisionless plasma - a high-temperature, low-density, ionized gas - is described by the Vlasov-Maxwell (VM) system. These equations are considered in one space dimension and two momentum dimensions without the assumption…

Analysis of PDEs · Mathematics 2016-04-18 Robert Glassey , Stephen Pankavich , Jack Schaeffer

We study the diffusive expansion for solutions around Maxwellian equilibrium and in a periodic box to the Vlasov-Maxwell-Boltzmann system, the most fundamental model for an ensemble of charged particles. Such an expansion yields a set of…

Analysis of PDEs · Mathematics 2007-05-23 Juhi Jang

The motion of a collisionless plasma - a high-temperature, low-density, ionized gas - is described by the Vlasov-Maxwell system. In the presence of large velocities, relativistic corrections are meaningful, and when symmetry of the particle…

Analysis of PDEs · Mathematics 2009-12-31 Robert Glassey , Stephen Pankavich , Jack Schaeffer
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