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841
On the existence of exponentially decreasing solutions of the nonlinear Landau damping problem
 Indiana Univ. Math. J
, 2009
"... Abstract. In this paper we prove the existence of a large class of periodic solutions of the VlasovPoisson in one space dimension that decay exponentially as t → ∞. The exponential decay is well known for the linearized version of the Landau damping problem. The results in this paper provide the f ..."
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Cited by 9 (0 self)
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the first example of solutions of the whole nonlinear VlasovPoisson system that exhibit such rate of decay. Keywords. Landau damping, VlasovPoisson system, exponential decay, analiticity properties of the solutions.
Nonlinear Stability in L^p for Solutions of the VlasovPoisson System for Charged Particles
"... We prove the nonlinear stability in L^p, with 1 p 2, of particular steady solutions of the VlasovPoisson system for charged particles in the whole space R^6. Our main tool is a functional related to the relative entropy or Casimirenergy functional. ..."
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Cited by 2 (1 self)
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We prove the nonlinear stability in L^p, with 1 p 2, of particular steady solutions of the VlasovPoisson system for charged particles in the whole space R^6. Our main tool is a functional related to the relative entropy or Casimirenergy functional.
Multiscale decomposition for VLASOVPOISSON EQUATIONS
, 2002
"... We consider the applications of a numericalanalytical approach based on multiscale variational wavelet technique to the systems with collective type behaviour described by some forms of VlasovPoisson/Maxwell equations. We calculate the exact fast convergent representations for solutions in highlo ..."
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We consider the applications of a numericalanalytical approach based on multiscale variational wavelet technique to the systems with collective type behaviour described by some forms of VlasovPoisson/Maxwell equations. We calculate the exact fast convergent representations for solutions in high
A discontinuous Galerkin method for the VlasovPoisson system
 J. Comput. Phys
, 2012
"... A discontinuous Galerkin method for approximating the VlasovPoisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions are used as a basis, the method preserves the positivity of ..."
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Cited by 18 (2 self)
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A discontinuous Galerkin method for approximating the VlasovPoisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions are used as a basis, the method preserves the positivity
Global existence and nonlinear stability for the relativistic VlasovPoisson system in the . . .
, 2008
"... ..."
Nonlinear instability of periodic BGK waves for VlasovPoisson system
 Comm. Pure Appl. Math
"... We investigate the nonlinear instability of periodic BernsteinGreeneKruskal(BGK) waves. Starting from an exponentially growing mode to the linearized equation, we proved nonlinear instability in the L1norm of the electric field. 1 ..."
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Cited by 4 (0 self)
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We investigate the nonlinear instability of periodic BernsteinGreeneKruskal(BGK) waves. Starting from an exponentially growing mode to the linearized equation, we proved nonlinear instability in the L1norm of the electric field. 1
Asymptotic behaviour for the VlasovPoisson System in the stellar dynamics case
 TMA
, 2003
"... We study an optimal inequality which relates potential and kinetic energies in an appropriate framework for bounded solutions of the VlasovPoisson (VP) system. Optimal distribution functions, which are completely characterized, minimize the total energy. From this variational approach, we deduce bo ..."
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Cited by 17 (10 self)
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We study an optimal inequality which relates potential and kinetic energies in an appropriate framework for bounded solutions of the VlasovPoisson (VP) system. Optimal distribution functions, which are completely characterized, minimize the total energy. From this variational approach, we deduce
An introduction to kinetic equations: the VlasovPoisson system and the Boltzmann equation, Discrete Contin
 Dyn. Syst
"... The purpose of kinetic equations is the description of dilute particle gases at an intermediate scale between the microscopic scale and the hydrodynamical scale. By dilute gases, one has to understand a system with a large number of particles, for which a description of the position and of the veloc ..."
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at the level of the phase space – at a statistical level – by a distribution function f(t,x,v). This course is intended to make an introductory review of the literature on kinetic equations. Only the most important ideas of the proofs will be given. The two main examples we shall use are the VlasovPoisson
A direct and accurate adaptive semiLagrangian scheme for the VlasovPoisson equation
 in "Applied Mathematics and Computer Science
, 2006
"... This article aims at giving a simplified presentation of a new adaptive semiLagrangian scheme for solving the (1 + 1)dimensional VlasovPoisson system, which was developed in 2005 with Michel Mehrenberger and first described in (Campos Pinto and Mehrenberger, 2007). The main steps of the analysis a ..."
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Cited by 1 (0 self)
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This article aims at giving a simplified presentation of a new adaptive semiLagrangian scheme for solving the (1 + 1)dimensional VlasovPoisson system, which was developed in 2005 with Michel Mehrenberger and first described in (Campos Pinto and Mehrenberger, 2007). The main steps of the analysis
2011 Stability of nonlinear Vlasov–Poisson equilibria through spectral deformation and Fourier–Hermite expansion
 Phys. Rev. E
"... We study the stability of spatially periodic, nonlinear VlasovPoisson equilibria as an eigenproblem in a FourierHermite basis (in the space and velocity variables, respectively) of finite dimension, N . When the advection term in the Vlasov equation is dominant, the convergence with N of the eige ..."
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We study the stability of spatially periodic, nonlinear VlasovPoisson equilibria as an eigenproblem in a FourierHermite basis (in the space and velocity variables, respectively) of finite dimension, N . When the advection term in the Vlasov equation is dominant, the convergence with N
Results 1  10
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841