Related papers: Approximate solutions for the Vlasov--Poisson syst…
This article is devoted to the Relativistic Vlasov-Maxwell system in space dimension three. We prove the local smooth solvability for weak topologies (and its long time version for small data). This result is derived from a representation…
We consider the Vlasov--Poisson system in a $C^3$ convex domain $D$ with a perfectly conducting wall. We introduce the asymptotic domain $D_{\infty}$ for the domain $D$. Then under acceptable assumptions on $D$, we show that for localized…
We analyse a diffuse interface type approximation, known as the diffuse domain approach, of a linear coupled bulk-surface elliptic partial differential system. The well-posedness of the diffuse domain approximation is shown using weighted…
It is known that when the diffuse interface thickness $\epsilon$ vanishes, the sharp interface limit of the stochastic reaction-diffusion equation is formally a stochastic geometric flow. To capture and simulate such geometric flow, it is…
We provide few remarks on nonlinear Landau damping that concerns decay of the electric field in the classical Vlasov-Poisson system near spatially homogenous equilibria. In particular, this includes the analyticity framework, \`a la…
In this work, we deal with the Vlasov-Poisson system in smooth physical domains with specular boundary condition, under mild integrability assumptions, and $d \ge 3$. We show that the Lagrangian and Eulerian descriptions of the system are…
The ionic Vlasov-Poisson-Boltzmann system is a fundamental model in dilute collisional plasmas. In this work, we study the compressible ionic Euler-Poisson limit of the ionic Vlasov-Poisson-Boltzmann system for the full range of cutoff…
The sequence of ground state energy density at finite size, e_{L}, provides much more information than usually believed. Having at disposal e_{L} for short lattice sizes, we show how to re-construct an approximate quasi-particle dispersion…
The boundary problem about behaviour (oscillations) of the electronic plasmas with arbitrary degree of degeneration of electronic gas in half-space with diffusion boundary conditions is analytically solved. The kinetic equation of Vlasov -…
The Vlasov-Poisson systems of equations (VP) describes the evolution of a distribution of collisionless particles under the effect of a collective-field potential. VP is at the basis of the study of the gravitational instability of…
When a plasma sheath forms next to a dielectric wall, material properties determine electron absorption and reflection from the surface, impacting the sheath formation and structure. The low energy regime of this interaction is often not…
Kinetic plasma simulations solve the Vlasov-Poisson or Vlasov-Maxwell equations to evolve scalar-variable distribution functions in position-velocity phase space and vector-variable electromagnetic fields in physical space. The…
In quasi-exactly solvable problems partial analytic solution (energy spectrum and associated wavefunctions) are obtained if some potential parameters are assigned specific values. We introduce a new class in which exact solutions are…
We consider a set of bipolar Euler-Poisson equations and study two asymptotic limiting processes. The first is the zero-electron-mass limit, which formally results in a non-linear adiabatic electron system. In a second step, we analyse the…
We study the linearized Vlasov-Poisson equation in the gravitational case around steady states that are decreasing and continuous functions of the energy. We identify the absolutely continuous spectrum and give criteria for the existence of…
We consider the linear stability problem for a 3D cylindrically symmetric equilibrium of the relativistic Vlasov-Maxwell system that describes a collisionless plasma. For an equilibrium whose distribution function decreases monotonically…
This article is devoted to the kinetic description in phase space of magnetically confined plasmas. It addresses the problem of stability near equilibria of the Relativistic Vlasov Maxwell system. We work under the Glassey-Strauss compactly…
The hybrid Vlasov-Maxwell system of equations is suitable to describe a magnetized plasma at scales of the order of or larger than proton kinetic scales. An exact stationary solution is presented by revisiting previous results with a…
A careful study of plasma-material interactions is essential to understand and improve the operation of devices where plasma contacts a wall. Key contributions of this work include (i) novel continuum kinetic algorithms with novel boundary…
The purpose of this paper is to mathematically investigate the formation of a plasma sheath near the surface of walls immersed in a plasma, and to analyze qualitative information of such a sheath layer. In the case of planar wall, Bohm…