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New Results in Velocity Averaging

François Golse (2001/2002)

Séminaire Équations aux dérivées partielles

This paper discusses two new directions in velocity averaging. One is an improvement of the known velocity averaging results for $L^{1}$ functions. The other shows how to adapt some of the ideas of velocity averaging to a situation that is essentially a new formulation of the Vlasov-Maxwell system.

Nonlinear models for laser-plasma interaction

Thierry Colin, Mathieu Colin, Guy Métivier (2006/2007)

Séminaire Équations aux dérivées partielles

In this paper, we present a nonlinear model for laser-plasma interaction describing the Raman amplification. This system is a quasilinear coupling of several Zakharov systems. We handle the Cauchy problem and we give some well-posedness and ill-posedness result for some subsystems.

Nonlinear stability of a spatially symmetric solution of the relativistic Poisson-Vlasov equation

Carlo Marchioro, Enrico Pagani (1987)

Rendiconti del Seminario Matematico della Università di Padova

Nonresonant smoothing for coupled wave + transport equations and the Vlasov-Maxwell system.

François Bouchut, François Golse, Christophe Pallard (2004)

Revista Matemática Iberoamericana

Numerical approximation of Knudsen layer for the Euler-Poisson system

Fréderique Charles, Nicolas Vauchelet, Christophe Besse, Thierry Goudon, Ingrid Lacroix–Violet, Jean-Paul Dudon, Laurent Navoret (2011)

ESAIM: Proceedings

In this work, we consider the computation of the boundary conditions for the linearized Euler–Poisson derived from the BGK kinetic model in the small mean free path regime. Boundary layers are generated from the fact that the incoming kinetic flux might be far from the thermodynamical equilibrium. In [2], the authors propose a method to compute numerically the boundary conditions in the hydrodynamic limit relying on an analysis of the boundary layers....

Numerical approximation of self-consistent Vlasov models for low-frequency electromagnetic phenomena

Nicolas Besse, Norbert J. mauser, Eric Sonnendrücker (2007)

International Journal of Applied Mathematics and Computer Science

We present a new numerical method to solve the Vlasov-Darwin and Vlasov-Poisswell systems which are approximations of the Vlasov-Maxwell equation in the asymptotic limit of the infinite speed of light. These systems model low-frequency electromagnetic phenomena in plasmas, and thus "light waves" are somewhat supressed, which in turn allows thenumerical discretization to dispense with the Courant-Friedrichs-Lewy condition on the time step. We construct a numerical scheme based on semi-Lagrangian...