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Results 1 - 10
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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 Vlasov-Poisson 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 Vlasov-Poisson system that exhibit such rate of decay. Keywords.- Landau damping, Vlasov-Poisson system, exponential decay, analiticity properties of the solutions.
Nonlinear Stability in L^p for Solutions of the Vlasov-Poisson System for Charged Particles
"... We prove the nonlinear stability in L^p, with 1 p 2, of particular steady solutions of the Vlasov-Poisson system for charged particles in the whole space R^6. Our main tool is a functional related to the relative entropy or Casimir-energy 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 Vlasov-Poisson system for charged particles in the whole space R^6. Our main tool is a functional related to the relative entropy or Casimir-energy functional.
Multiscale decomposition for VLASOV-POISSON EQUATIONS
, 2002
"... We consider the applications of a numerical-analytical approach based on multiscale variational wavelet technique to the systems with collective type behaviour described by some forms of Vlasov-Poisson/Maxwell equations. We calculate the exact fast convergent representations for solutions in high-lo ..."
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We consider the applications of a numerical-analytical approach based on multiscale variational wavelet technique to the systems with collective type behaviour described by some forms of Vlasov-Poisson/Maxwell equations. We calculate the exact fast convergent representations for solutions in high
A discontinuous Galerkin method for the Vlasov-Poisson system
- J. Comput. Phys
, 2012
"... A discontinuous Galerkin method for approximating the Vlasov-Poisson 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 Vlasov-Poisson 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 Vlasov-Poisson system in the . . .
, 2008
"... ..."
Nonlinear instability of periodic BGK waves for Vlasov-Poisson system
- Comm. Pure Appl. Math
"... We investigate the nonlinear instability of periodic Bernstein-Greene-Kruskal(BGK) waves. Starting from an exponentially growing mode to the linearized equation, we proved nonlinear instability in the L1-norm 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 Bernstein-Greene-Kruskal(BGK) waves. Starting from an exponentially growing mode to the linearized equation, we proved nonlinear instability in the L1-norm of the electric field. 1
Asymptotic behaviour for the Vlasov-Poisson 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 Vlasov-Poisson (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 Vlasov-Poisson (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 Vlasov-Poisson 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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Cited by 4 (0 self)
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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 Vlasov-Poisson
A direct and accurate adaptive semi-Lagrangian scheme for the Vlasov-Poisson equation
- in "Applied Mathematics and Computer Science
, 2006
"... This article aims at giving a simplified presentation of a new adaptive semi-Lagrangian scheme for solving the (1 + 1)dimensional Vlasov-Poisson 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 semi-Lagrangian scheme for solving the (1 + 1)dimensional Vlasov-Poisson 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 Vlasov-Poisson equilibria as an eigenproblem in a Fourier-Hermite 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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Cited by 1 (0 self)
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We study the stability of spatially periodic, nonlinear Vlasov-Poisson equilibria as an eigenproblem in a Fourier-Hermite 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
of
841
