Some controllability results for the relativistic Vlasov-Maxwell system
Journées équations aux dérivées partielles (2012), article no. 5, 12 p.

The goal of this note is to present the recent results concerning the controllability of the Vlasov-Maxwell system, which are proved in the paper [10] by Olivier Glass and the author.

L’objectif de cette note est de présenter les résultats récents concernant la contrôlabilité du système de Vlasov-Maxwell, qui sont prouvés dans le papier [10] écrit en collaboration avec Olivier Glass.

DOI: 10.5802/jedp.88
Classification: 35Q83, 93B05
Keywords: Vlasov-Maxwell equations, controllability, geometric control condition
Mot clés : Equations de Vlasov-Maxwell, contrôlabilité, condition de contrôle géométrique
Han-Kwan, Daniel 1

1 DMA Ecole Normale SupŽrieure 45 rue d’Ulm 75005 Paris France
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Han-Kwan, Daniel. Some controllability results for the relativistic Vlasov-Maxwell system. Journées équations aux dérivées partielles (2012), article  no. 5, 12 p. doi : 10.5802/jedp.88. http://www.numdam.org/articles/10.5802/jedp.88/

[1] Asano, K. On local solutions of the initial value problem for the Vlasov-Maxwell equation, Comm. Math. Phys., Volume 106 (1986) no. 4, pp. 551-568 http://projecteuclid.org/getRecord?id=euclid.cmp/1104115851 | MR | Zbl

[2] Asano, K.; Ukai, S. On the Vlasov-Poisson limit of the Vlasov-Maxwell equation, Patterns and waves (Stud. Math. Appl.), Volume 18, North-Holland, Amsterdam, 1986, pp. 369-383 | MR | Zbl

[3] Bardos, C.; Lebeau, G.; Rauch, J. Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary, SIAM J. Control Optim., Volume 30 (1992) no. 5, pp. 1024-1065 | DOI | MR | Zbl

[4] Burq, N.; Gérard, P. Condition nécessaire et suffisante pour la contrôlabilité exacte des ondes, C. R. Acad. Sci. Paris Sér. I Math., Volume 325 (1997) no. 7, pp. 749-752 | DOI | MR | Zbl

[5] Coron, J.-M. Control and nonlinearity, Mathematical Surveys and Monographs, 136, American Mathematical Society, Providence, RI, 2007 | MR | Zbl

[6] Degond, P. Local existence of solutions of the Vlasov-Maxwell equations and convergence to the Vlasov-Poisson equations for infinite light velocity, Math. Methods Appl. Sci., Volume 8 (1986) no. 4, pp. 533-558 | DOI | MR | Zbl

[7] Ervedoza, S.; Zuazua, E. A systematic method for building smooth controls for smooth data, Discrete Contin. Dyn. Syst. Ser. B, Volume 14 (2010) no. 4, pp. 1375-1401 | DOI | MR | Zbl

[8] Glass, O. On the controllability of the Vlasov-Poisson system, J. Differential Equations, Volume 195 (2003) no. 2, pp. 332-379 | DOI | MR | Zbl

[9] Glass, O. LA MÉTHODE DU RETOUR EN CONTRoLABILITÉ ET SES APPLICATIONS EN MÉCANIQUE DES FLUIDES, Séminaire Bourbaki (2010)

[10] Glass, O.; Han-Kwan, D. On the controllability of the relativistic Vlasov-Maxwell system, Preprint (2012) | MR

[11] Glass, O.; Han-Kwan, D. On the controllability of the Vlasov-Poisson system in the presence of external force fields, J. Differential Equations, Volume 252 (2012) no. 10, pp. 5453-5491 | MR | Zbl

[12] Glassey, R.; Strauss, W. Singularity formation in a collisionless plasma could occur only at high velocities, Arch. Rational Mech. Anal., Volume 92 (1986) no. 1, pp. 59-90 | DOI | MR | Zbl

[13] Phung, K. D. Contrôle et stabilisation d’ondes électromagnétiques, ESAIM Control Optim. Calc. Var., Volume 5 (2000), p. 87-137 (electronic) | DOI | Numdam | MR | Zbl

[14] Rauch, J.; Taylor, M. Exponential decay of solutions to hyperbolic equations in bounded domains, Indiana Univ. Math. J., Volume 24 (1974), pp. 79-86 | MR | Zbl

[15] Schaeffer, J. The classical limit of the relativistic Vlasov-Maxwell system, Comm. Math. Phys., Volume 104 (1986) no. 3, pp. 403-421 http://projecteuclid.org/getRecord?id=euclid.cmp/1104115084 | MR | Zbl

[16] Wollman, S. An existence and uniqueness theorem for the Vlasov-Maxwell system, Comm. Pure Appl. Math., Volume 37 (1984) no. 4, pp. 457-462 | DOI | MR | Zbl

[17] Wollman, S. Local existence and uniqueness theory of the Vlasov-Maxwell system, J. Math. Anal. Appl., Volume 127 (1987) no. 1, pp. 103-121 | DOI | MR | Zbl

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