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Application of Lie transform techniques for simulation of a charged particle beam
Geometric two-scale convergence on manifold and applications to the Vlasov equation
1. | Centre de physique théorique-CNRS, Campus de Luminy, Case 907 13288 Marseille cedex 9, France |
2. | LMBA (UMR 6205) Université de Bretagne-Sud, Campus de Tohannic, 56000 Vannes, France |
References:
[1] |
G. Allaire, Homogenization and two-scale convergence, SIAM J. Math. Anal., 23 (1992), 1482-1518.
doi: 10.1137/0523084. |
[2] |
A. Back, Étude Théorique et Numérique Des Équations de Vlasov-Maxwell Dans le Formalisme Covariant, (French) Ph.D Thesis, 2011. |
[3] |
G. D. Birkhoff, What is the ergodic theorem?, Amer. Math. Monthly, 49 (1942), 222-226.
doi: 10.2307/2303229. |
[4] |
E. Frénod and E. Sonnendrücker, The finite Larmor radius approximation, SIAM J. Math. Anal., 32 (2001), 1227-1247.
doi: 10.1137/S0036141099364243. |
[5] |
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 (1998), 193-213. |
[6] |
E. Frénod and P.-A. Raviart and E. Sonnendrücker, Two-scale expansion of a singularly perturbed convection equation, J. Math. Pures Appl., 80 (2001), 815-843.
doi: 10.1016/S0021-7824(01)01215-6. |
[7] |
D. Han-Kwan, The three-dimensional finite Larmor radius approximation, Asymptot. Anal., 66 (2010), 9-33. |
[8] |
E. Hopf, Statistik Der Geodätischen Linien in Mannigfaltigkeiten Negativer Krümmung, Ber. Verh. Sächs. Akad. Wiss. Leipzig, 1939. |
[9] |
J. Jost, Riemannian Geometry and Geometric Analysis, Fifth edition, Universitext, Springer-Verlag, Berlin, 2008. |
[10] |
F. I. Mautner, Geodesic flows on symmetric Riemann spaces, Ann. of Math., 65 (1957), 416-431.
doi: 10.2307/1970054. |
[11] |
G. Nguetseng, A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal., 20 (1989), 608-623.
doi: 10.1137/0520043. |
[12] |
H. C. Pak, Geometric two-scale convergence on forms and its applications to Maxwell's equations, Proc. R. Soc. Edinb., Sect. A, Math., 135 (2005), 133-157.
doi: 10.1017/S0308210500003802. |
[13] |
C. H. Scott, $L^p$ theory of differential forms on manifolds, Trans. Amer. Math. Soc., 347 (1995), 2075-2096.
doi: 10.2307/2154923. |
[14] |
C. H. Scott, $L^p$ Theory of Differential Forms on Manifolds, ProQuest LLC, Ann Arbor, MI, 1993. |
show all references
References:
[1] |
G. Allaire, Homogenization and two-scale convergence, SIAM J. Math. Anal., 23 (1992), 1482-1518.
doi: 10.1137/0523084. |
[2] |
A. Back, Étude Théorique et Numérique Des Équations de Vlasov-Maxwell Dans le Formalisme Covariant, (French) Ph.D Thesis, 2011. |
[3] |
G. D. Birkhoff, What is the ergodic theorem?, Amer. Math. Monthly, 49 (1942), 222-226.
doi: 10.2307/2303229. |
[4] |
E. Frénod and E. Sonnendrücker, The finite Larmor radius approximation, SIAM J. Math. Anal., 32 (2001), 1227-1247.
doi: 10.1137/S0036141099364243. |
[5] |
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 (1998), 193-213. |
[6] |
E. Frénod and P.-A. Raviart and E. Sonnendrücker, Two-scale expansion of a singularly perturbed convection equation, J. Math. Pures Appl., 80 (2001), 815-843.
doi: 10.1016/S0021-7824(01)01215-6. |
[7] |
D. Han-Kwan, The three-dimensional finite Larmor radius approximation, Asymptot. Anal., 66 (2010), 9-33. |
[8] |
E. Hopf, Statistik Der Geodätischen Linien in Mannigfaltigkeiten Negativer Krümmung, Ber. Verh. Sächs. Akad. Wiss. Leipzig, 1939. |
[9] |
J. Jost, Riemannian Geometry and Geometric Analysis, Fifth edition, Universitext, Springer-Verlag, Berlin, 2008. |
[10] |
F. I. Mautner, Geodesic flows on symmetric Riemann spaces, Ann. of Math., 65 (1957), 416-431.
doi: 10.2307/1970054. |
[11] |
G. Nguetseng, A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal., 20 (1989), 608-623.
doi: 10.1137/0520043. |
[12] |
H. C. Pak, Geometric two-scale convergence on forms and its applications to Maxwell's equations, Proc. R. Soc. Edinb., Sect. A, Math., 135 (2005), 133-157.
doi: 10.1017/S0308210500003802. |
[13] |
C. H. Scott, $L^p$ theory of differential forms on manifolds, Trans. Amer. Math. Soc., 347 (1995), 2075-2096.
doi: 10.2307/2154923. |
[14] |
C. H. Scott, $L^p$ Theory of Differential Forms on Manifolds, ProQuest LLC, Ann Arbor, MI, 1993. |
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