Journal of Pure and Applied Mathematics: Advances and Applications[1] R. Adams and J. Fournier, Sobolev Spaces, Academic Press,
(1975-2nd ed. in 2003).
[2] P. Ailliot, E. Frénod and V. Monbet, Long term object drift in
the ocean with tide and wind, Multiscale Model. Simul. 5(2) (2006),
514-531.
[3] G. Allaire, Homogenization and two-scale convergence, SIAM J.
Math. Anal. 23(6) (1992), 1482-1518.
[4] N. Besse and E. Sonnendrücker, Semi-Lagrangian schemes for the
Vlasov equation on an unstructured mesh of phase space, J. Comp. Phys.
191 (2003), 341-376.
[5] M. Bostan, The Vlasov-Poisson system with strong external magnetic
field, finite Larmor radius regime, Asymptot. Anal. 61(2) (2007),
91-123.
[6] A. Brizard, Nonlinear Gyrokinetic Tokamak Physics, PhD thesis of
Princeton University, 1990.
[7] A. Brizard and T.-S. Hahm, Foundations of nonlinear gyrokinetic
theory, Rev. Mod. Phys. 79 (2007), 421-468.
[8] D.-H. Dubin, J.-A. Krommes, C. Oberman and W.-W. Lee, Nonlinear
gyrokinetic equations, Phys. Fluids 26(12) (1983), 3524-3535.
[9] E. Frénod and E. Sonnendrücker, Homogenization of the Vlasov
equation and of the Vlasov-Poisson system with a strong external
magnetic field, Asymptot. Anal. 18(3-4) (1998), 193-214.
[10] E. Frénod and E. Sonnendrücker, Long time behavior of the
Vlasov equation with a strong external magnetic field, Math. Models
Methods Appl. Sci. 10(4) (2000), 539-553.
[11] E. Frénod and E. Sonnendrücker, The finite Larmor radius
approximation, SIAM J. Math. Anal. 32(6) (2001), 1227-1247.
[12] E. Frénod, P.-A. Raviart and E. Sonnendrücker, Two-scale
expansion of a singularly perturbed convection equation, J. Math.
Pures Appl. 80(8) (2001), 815-843.
[13] E. Frénod, A. Mouton and E. Sonnendrücker, Two-scale numerical
simulation of the weakly compressible 1D isentropic Euler equations,
Numer. Math. 108(2) (2007), 263-293.
[14] E. Frénod, F. Salvarani and E. Sonnendrücker, Long time
simulation of a beam in a periodic focusing channel via a two-scale
PIC-method, Math. Models Methods Appl. Sci. 19(2) (2009), 175-197.
[15] F. Golse and L. Saint-Raymond, The Vlasov-Poisson system with
strong magnetic field, J. Math. Pures Appl. 78 (1999), 791-817.
[16] F. Golse and L. Saint-Raymond, The Vlasov-Poisson system with
strong magnetic field in quasineutral regime, Math. Models Methods
Appl. Sci. 13(5) (2003), 661-714.
[17] V. Grandgirard, M. Brunetti, P. Bertrand, N. Besse, X. Garbet, P.
Ghendrih, G. Manfredi, Y. Sarazin, O. Sauter, E. Sonnendrücker, J.
Vaclavik and L. Villard, A drift-kinetic semi-Lagrangian 4D code for
ion turbulence simulation, J. Comp. Phys. 217 (2006), 395-423.
[18] D. Han-Kwan, The three-dimensional finite Larmor radius
approximation, Asymptot. Anal. 66(1) (2010), 9-33.
[19] W.-W. Lee, Gyrokinetic approach in particle simulation, Phys.
Fluids 26(2) (1983), 555-562.
[20] W.-W. Lee, Gyrokinetic particle simulation model, J. Comp. Phys.
72(1) (1987), 243-269.
[21] J.-L. Lions, Quelques Méthodes de Résolution de Problèmes aux
Limites Non Linéaires, Dunod, Gauthier-Villars, 1969.
[22] R.-G. Littlejohn, A guiding center Hamiltonian: A new approach,
J. Math. Phys. 20(12) (1979), 2445-2458.
[23] A. Mouton, Approximation multi-échelles de l’équation de
Vlasov, thèse de l’Université de Strasbourg, Éd. Universitaires
Européennes, TEL-00411964 (2009).
[24] A. Mouton, Two-scale semi-Lagrangian simulation of a charged
particle beam in a periodic focusing channel, Kinet. Relat. Models
2(2) (2009), 251-274.
[25] G. Nguetseng, A general convergence result for a functional
related to the theory of homogenization, SIAM J. Math. Anal. 20(3)
(1989), 608-623.
