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We study smooth, global-in-time solutions of the Vlasov-Poisson system in the plasma physical case that possess arbitrarily large charge densities and electric fields. In particular, we construct two classes of solutions with this property.…

Analysis of PDEs · Mathematics 2017-08-09 Jonathan Ben-Artzi , Simone Calogero , Stephen Pankavich

Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…

Pattern Formation and Solitons · Physics 2021-05-14 Andrew L. Krause , Václav Klika , Philip K. Maini , Denis Headon , Eamonn A. Gaffney

We consider relativistic plasma particles subjected to an external gravitation force in a $3$D half space whose boundary is a perfect conductor. When the mean free path is much bigger than the variation of electromagnetic fields, the…

Analysis of PDEs · Mathematics 2022-03-04 Yunbai Cao , Chanwoo Kim

A collisionless plasma is modeled by the Vlasov-Poisson system in one dimension. We consider the situation in which mobile negative ions balance a fixed background of positive charge, which is independent of space and time, as x tends to…

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

A multispecies, collisionless plasma is modeled by the Vlasov-Poisson system. Assuming the plasma is neutral and the electric field decays with sufficient rapidity as $t \to\infty$, we show that solutions can be constructed with arbitrarily…

Analysis of PDEs · Mathematics 2025-02-06 Grace Mattingly , Stephen Pankavich , Jonathan Ben-Artzi

We study existence and uniqueness of the solution to the Vlasov-Poisson system describing a plasma constituted by different species evolving in $\mathbb{R}^3$, whose particles interact via the Coulomb potential. The species can have both…

Mathematical Physics · Physics 2019-12-03 Silvia Caprino , Guido Cavallaro , Carlo Marchioro

We address the existence of stationary solutions of the Vlasov-Poisson system on a domain $\Omega\subset\mathbb{R}^3$ describing a high-temperature plasma which due to the influence of an external magnetic field is spatially confined to a…

Analysis of PDEs · Mathematics 2021-05-25 Yulia O. Belyaeva , Björn Gebhard , Alexander L. Skubachevskii

The control of plasma-wall interactions is crucial to fusion devices from both physical and mathematical perspectives. It is well known that a magnetic field satisfying the classical perfect conducting conditions at the wall, $$ \mathbf{E}…

Analysis of PDEs · Mathematics 2024-12-17 Hongjie Dong , Yan Guo , Timur Yastrzhembskiy

Motivated by the stellar wind ejected from the upper atmosphere (Corona) of a star, we explore a boundary problem of the two-species nonlinear relativistic Vlasov-Poisson systems in the 3D half space in the presence of a constant vertical…

Analysis of PDEs · Mathematics 2024-09-04 Jiaxin Jin , Chanwoo Kim

We consider the Boltzmann equation with external fields in strictly convex domains with diffuse reflection boundary condition. As long as the normal derivative of external fields satisfy some sign condition on the boundary (1.8) we…

Analysis of PDEs · Mathematics 2019-06-04 Yunbai Cao

This work concerns the Vlasov-Poisson-Boltzmann system without angular cutoff and Vlasov-Poisson-Landau system including Coulomb interaction in bounded domain, namely union of cubes. We establish the global stability, exponential large-time…

Analysis of PDEs · Mathematics 2022-08-24 Dingqun Deng

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

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 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

The two-dimensional one-component plasma at the special coupling \beta = 2 is known to be exactly solvable, for its free energy and all of its correlations, on a variety of surfaces and with various boundary conditions. Here we study this…

Mathematical Physics · Physics 2016-11-25 Jonit Fischmann , Peter J. Forrester

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

The time evolution of a collisionless plasma is modeled by the Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We only consider a 'two-dimensional' version of…

Optimization and Control · Mathematics 2021-03-02 Jörg Weber

This paper investigates a class of chemotaxis systems modeling lethal interactions in a smooth, bounded domain $\Omega \subset \mathbb{R}^n$ with homogeneous Neumann boundary conditions. We examine two distinct cases: (i) a fully parabolic…

Analysis of PDEs · Mathematics 2026-02-06 Gnanasekaran Shanmugasundaram , Jitraj Saha

The relativistic Vlasov-Maxwell system describes the evolution of a collisionless plasma. The problem of linear instability of this system is considered in two physical settings: the so-called "one and one-half" dimensional case, and the…

Analysis of PDEs · Mathematics 2015-05-22 Jonathan Ben-Artzi , Thomas Holding

The Vlasov-Poisson-Boltzmann equation is a classical equation governing the dynamics of charged particles with the electric force being self-imposed. We consider the system in a convex domain with the Cercignani-Lampis boundary condition.…

Analysis of PDEs · Mathematics 2021-04-07 Hongxu Chen , Chanwoo Kim , Qin Li