Solutions périodiques en temps des équations de Vlasov–Maxwell

Mihai Bostan

doi:10.1016/j.crma.2004.07.008

Physique mathématique

Solutions périodiques en temps des équations de Vlasov–Maxwell
[Time periodic solutions for the Vlasov–Maxwell equations.]

Presented by: Philippe G. Ciarlet

Mihai Bostan ¹

¹ Laboratoire de mathématiques de Besançon, UMR CNRS 6623, université de Franche-Comté, 16, route de Gray, 25030 Besançon cedex, France

Comptes Rendus. Mathématique, Volume 339 (2004) no. 6, pp. 451-456.

Abstract
Résumé

We study here the existence of time periodic solution for the Vlasov–Maxwell equations in a three dimensional bounded domain. We assume that the boundary of the domain is strictly star-shaped. We give a priori estimates for the kinetic and electro-magnetic energy, and also for the normal and tangential traces of the electro-magnetic field. This method allows us to treat both classical and relativistic cases.

Nous étudions l'existence de solution périodique en temps pour les équations de Vlasov–Maxwell dans un domaine borné tridimensionnel. On suppose que la frontière du domaine est strictement étoilée. Nous donnons également des estimations a priori pour l'énergie cinétique et électromagnétique ainsi que pour les traces normales et tangentielles du champ électromagnétique. La méthode utilisée permet de traiter à la fois les cas classique et relativiste.

Received: 2004-06-19
Accepted: 2004-07-12
Published online: 2004-09-09

DOI: 10.1016/j.crma.2004.07.008

Author's affiliations:

Mihai Bostan ¹

¹ Laboratoire de mathématiques de Besançon, UMR CNRS 6623, université de Franche-Comté, 16, route de Gray, 25030 Besançon cedex, France

@article{CRMATH_2004__339_6_451_0,
     author = {Mihai Bostan},
     title = {Solutions p\'eriodiques en temps des \'equations de {Vlasov{\textendash}Maxwell}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {451--456},
     publisher = {Elsevier},
     volume = {339},
     number = {6},
     year = {2004},
     doi = {10.1016/j.crma.2004.07.008},
     language = {fr},
}

TY  - JOUR
AU  - Mihai Bostan
TI  - Solutions périodiques en temps des équations de Vlasov–Maxwell
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 451
EP  - 456
VL  - 339
IS  - 6
PB  - Elsevier
DO  - 10.1016/j.crma.2004.07.008
LA  - fr
ID  - CRMATH_2004__339_6_451_0
ER  -

%0 Journal Article
%A Mihai Bostan
%T Solutions périodiques en temps des équations de Vlasov–Maxwell
%J Comptes Rendus. Mathématique
%D 2004
%P 451-456
%V 339
%N 6
%I Elsevier
%R 10.1016/j.crma.2004.07.008
%G fr
%F CRMATH_2004__339_6_451_0

Mihai Bostan. Solutions périodiques en temps des équations de Vlasov–Maxwell. Comptes Rendus. Mathématique, Volume 339 (2004) no. 6, pp. 451-456. doi : 10.1016/j.crma.2004.07.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.07.008/

References
Cited by

[1] A. Arseneev Global existence of a weak solution of the Vlasov system of equations, URSS Comput. Math. Phys., Volume 15 (1975), pp. 131-143

[2] N. Ben Abdallah Weak solutions of the initial-boundary value problem for the Vlasov–Poisson system, Math. Methods Appl. Sci., Volume 17 (1994) no. 6, pp. 451-476

[3] M. Bostan; F. Poupaud Periodic solutions of the 1D Vlasov–Maxwell system with boundary conditions, Math. Methods Appl. Sci., Volume 23 (2000), pp. 1195-1221

[4] M. Bostan Permanent regimes for the 1D Vlasov–Poisson system with boundary conditions, SIAM J. Math. Anal., Volume 35 (2003) no. 4, pp. 922-948

[5] M. Bostan, Boundary value problem for the N dimensional time periodic Vlasov–Poisson system, soumis

[6] M. Bostan, Boundary value problem for the three dimensional time periodic Vlasov–Maxwell system, en préparation

[7] R.J. Diperna; P.L. Lions Global weak solutions of the Vlasov–Maxwell system, Commun. Pure Appl. Math., Volume XVII (1989), pp. 729-757

[8] C. Greengard; P.-A. Raviart A boundary value problem for the stationary Vlasov–Poisson equations: the plane diode, Commun. Pure Appl. Math., Volume XLIII (1990), pp. 473-507

[9] Y. Guo Global weak solutions of the Vlasov–Maxwell system with boundary conditions, Commun. Math. Phys., Volume 154 (1993), pp. 245-263

[10] V. Komornik Exact Controllability and Stabilization. The Multiplier Method, RAM, Masson, Paris, 1994

[11] P.-L. Lions; B. Perthame Propagation of moments and regularity for the 3-dimensional Vlasov–Poisson system, Invent. Math., Volume 105 (1991), pp. 415-430

[12] F. Poupaud Boundary value problems for the stationary Vlasov–Maxwell system, Forum Math., Volume 4 (1992), pp. 499-527

[13] T. Ukai; S. Okabe On the classical solution in the large time of the two dimensional Vlasov equations, Osaka J. Math., Volume 15 (1978), pp. 245-261

Cited by Sources:

Comments - Policy