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.
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.
@article{JEDP_2012____A5_0, author = {Han-Kwan, Daniel}, title = {Some controllability results for the relativistic Vlasov-Maxwell system}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, year = {2012}, pages = {1-12}, doi = {10.5802/jedp.88}, language = {en}, url = {http://dml.mathdoc.fr/item/JEDP_2012____A5_0} }
Han-Kwan, Daniel. Some controllability results for the relativistic Vlasov-Maxwell system. Journées équations aux dérivées partielles, (2012), pp. 1-12. doi : 10.5802/jedp.88. http://gdmltest.u-ga.fr/item/JEDP_2012____A5_0/
[1] On local solutions of the initial value problem for the Vlasov-Maxwell equation, Comm. Math. Phys., Tome 106 (1986) no. 4, pp. 551-568 http://projecteuclid.org/getRecord?id=euclid.cmp/1104115851 | MR 860309 | Zbl 0631.76090
[2] On the Vlasov-Poisson limit of the Vlasov-Maxwell equation, Patterns and waves, North-Holland, Amsterdam (Stud. Math. Appl.) Tome 18 (1986), pp. 369-383 | MR 882384 | Zbl 0623.35059
[3] Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary, SIAM J. Control Optim., Tome 30 (1992) no. 5, pp. 1024-1065 | Article | MR 1178650 | Zbl 0786.93009
[4] Condition nécessaire et suffisante pour la contrôlabilité exacte des ondes, C. R. Acad. Sci. Paris Sér. I Math., Tome 325 (1997) no. 7, pp. 749-752 | Article | MR 1483711 | Zbl 0906.93008
[5] Control and nonlinearity, American Mathematical Society, Providence, RI, Mathematical Surveys and Monographs, Tome 136 (2007) | MR 2302744 | Zbl 1140.93002
[6] Local existence of solutions of the Vlasov-Maxwell equations and convergence to the Vlasov-Poisson equations for infinite light velocity, Math. Methods Appl. Sci., Tome 8 (1986) no. 4, pp. 533-558 | Article | MR 870991 | Zbl 0619.35088
[7] A systematic method for building smooth controls for smooth data, Discrete Contin. Dyn. Syst. Ser. B, Tome 14 (2010) no. 4, pp. 1375-1401 | Article | MR 2679646 | Zbl 1219.93011
[8] On the controllability of the Vlasov-Poisson system, J. Differential Equations, Tome 195 (2003) no. 2, pp. 332-379 | Article | MR 2016816 | Zbl 1109.93007
[9] LA MÉTHODE DU RETOUR EN CONTRoLABILITÉ ET SES APPLICATIONS EN MÉCANIQUE DES FLUIDES, Séminaire Bourbaki (2010) | Zbl pre06149575
[10] On the controllability of the relativistic Vlasov-Maxwell system, Preprint (2012) | MR 2902122
[11] On the controllability of the Vlasov-Poisson system in the presence of external force fields, J. Differential Equations, Tome 252 (2012) no. 10, pp. 5453-5491 | MR 2902122 | Zbl 1238.35160
[12] Singularity formation in a collisionless plasma could occur only at high velocities, Arch. Rational Mech. Anal., Tome 92 (1986) no. 1, pp. 59-90 | Article | MR 816621 | Zbl 0595.35072
[13] Contrôle et stabilisation d’ondes électromagnétiques, ESAIM Control Optim. Calc. Var., Tome 5 (2000), p. 87-137 (electronic) | Article | Numdam | MR 1744608 | Zbl 0942.93002
[14] Exponential decay of solutions to hyperbolic equations in bounded domains, Indiana Univ. Math. J., Tome 24 (1974), pp. 79-86 | MR 361461 | Zbl 0281.35012
[15] The classical limit of the relativistic Vlasov-Maxwell system, Comm. Math. Phys., Tome 104 (1986) no. 3, pp. 403-421 http://projecteuclid.org/getRecord?id=euclid.cmp/1104115084 | MR 840744 | Zbl 0597.35109
[16] An existence and uniqueness theorem for the Vlasov-Maxwell system, Comm. Pure Appl. Math., Tome 37 (1984) no. 4, pp. 457-462 | Article | MR 745326 | Zbl 0592.45010
[17] Local existence and uniqueness theory of the Vlasov-Maxwell system, J. Math. Anal. Appl., Tome 127 (1987) no. 1, pp. 103-121 | Article | MR 904213 | Zbl 0645.35013