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Related papers: The Vlasov-Poisson-Boltzmann System for Soft Poten…

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Two fundamental models in plasma physics are given by the Vlasov-Poisson-Landau system and the compressible Euler-Poisson system which both capture the complex dynamics of plasmas under the self-consistent electric field interactions at the…

Analysis of PDEs · Mathematics 2023-08-21 Renjun Duan , Dongcheng Yang , Hongjun Yu

We are interested in a kinetic equation intended to describe the interaction of particles with their environment. The environment is modeled by a collection of local vibrational degrees of freedom. We establish the existence of weak…

Analysis of PDEs · Mathematics 2016-03-14 Stephan De Bièvre , Arthur Vavasseur , Thierry Goudon

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

The relaxation of a weakly collisional plasma, which is of fundamental interest to laboratory and astrophysical plasmas, can be described by the Boltzmann-Poisson equations with the Lenard-Bernstein collision operator. We perform a…

Plasma Physics · Physics 2024-11-13 Uddipan Banik , Amitava Bhattacharjee

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

We study, globaly in time, the velocity distribution $f(v,t)$ of a spatially homogeneous system that models a system of electrons in a weakly ionized plasma, subjected to a constant external electric field $E$. The density $f$ satisfies a…

Plasma Physics · Physics 2009-10-30 E. Carlen , R. Esposito , J. L. Lebowitz , R. Marra , A. Rokhlenko

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

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

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

A collisionless plasma is modeled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge - dependant upon only velocity - is assumed. The situation in which mobile negative ions balance the positive…

Analysis of PDEs · Mathematics 2010-01-06 Stephen Pankavich

The Cauchy problem for the Boltzmann equation with soft potential, in the framework of small perturbation of an equilibrium state, has been studied in many spaces. The method of strongly continuous semigroup has been applied by…

Analysis of PDEs · Mathematics 2024-02-08 Dingqun Deng

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…

Analysis of PDEs · Mathematics 2016-08-16 José A. Carrillo , Simon Labrunie

We study smooth, spherically-symmetric solutions to the Vlasov-Poisson system and relativistic Vlasov-Poisson system in the plasma physical case. We construct solutions that initially possess arbitrarily small C^k norms for the charge…

Analysis of PDEs · Mathematics 2019-10-15 Katherine Zhiyuan Zhang

We construct a mean-field model that describes the nonlinear dynamics of a spin-polarized electron gas interacting with fixed, positively-charged ions possessing a magnetic moment that evolves in time. The mobile electrons are modeled by a…

We consider a quasilinear system of hyperbolic equations that describes plane one-dimensional non-relativistic oscillations of electrons in a cold plasma with allowance for electron-ion collisions. Accounting for collisions leads to the…

Mathematical Physics · Physics 2021-01-08 Olga Rozanova , Eugeniy Chizhonkov , Maria Delova

A fundamental two-fluid model for describing dynamics of a plasma is the Euler-Poisson system, in which compressible ion and electron fluids interact with their self-consistent electrostatic force. Global smooth electron dynamics were…

Mathematical Physics · Physics 2015-05-18 Yan Guo , Benoit Pausader

A multispecies, collisionless plasma is modeled by the Vlasov-Poisson system. Assuming that the electric field decays with sufficient rapidity as $t \to\infty$, we show that the velocity characteristics and spatial averages of the particle…

Analysis of PDEs · Mathematics 2022-01-25 Stephen Pankavich

This paper is devoted to the study of the nonlinear stability of the rarefaction waves of the Vlasov-Poisson-Boltzmann system with slab symmetry in the case where the electron background density satisfies an analogue of the Boltzmann…

Analysis of PDEs · Mathematics 2014-05-13 Renjun Duan , Shuangqian Liu

A collisionless plasma is modeled by the Vlasov-Poisson system in one-dimension. A fixed background of positive charge, dependent only upon velocity, is assumed and the situation in which the mobile negative ions balance the positive charge…

Analysis of PDEs · Mathematics 2010-03-01 Stephen Pankavich

The one-dimensional Vlasov-Poisson system is considered and a particle method is developed to approximate solutions without compact support which tend to a fixed background of charge as $| x | \to \infty$. Such a system of equations can be…

Numerical Analysis · Mathematics 2014-01-03 Stephen Pankavich