Some controllability results for the relativistic Vlasov-Maxwell system

Daniel Han-Kwan[1]

  • [1] DMA Ecole Normale SupŽrieure 45 rue d’Ulm 75005 Paris France

Journées Équations aux dérivées partielles (2012)

  • page 1-12
  • ISSN: 0752-0360

Abstract

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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.

How to cite

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Han-Kwan, Daniel. "Some controllability results for the relativistic Vlasov-Maxwell system." Journées Équations aux dérivées partielles (2012): 1-12. <http://eudml.org/doc/275538>.

@article{Han2012,
abstract = {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.},
affiliation = {DMA Ecole Normale SupŽrieure 45 rue d’Ulm 75005 Paris France},
author = {Han-Kwan, Daniel},
journal = {Journées Équations aux dérivées partielles},
keywords = {Vlasov-Maxwell equations; controllability; geometric control condition},
language = {eng},
pages = {1-12},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Some controllability results for the relativistic Vlasov-Maxwell system},
url = {http://eudml.org/doc/275538},
year = {2012},
}

TY - JOUR
AU - Han-Kwan, Daniel
TI - Some controllability results for the relativistic Vlasov-Maxwell system
JO - Journées Équations aux dérivées partielles
PY - 2012
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 12
AB - 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.
LA - eng
KW - Vlasov-Maxwell equations; controllability; geometric control condition
UR - http://eudml.org/doc/275538
ER -

References

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  1. K. Asano, On local solutions of the initial value problem for the Vlasov-Maxwell equation, Comm. Math. Phys. 106 (1986), 551-568 Zbl0631.76090MR860309
  2. K. Asano, S. Ukai, On the Vlasov-Poisson limit of the Vlasov-Maxwell equation, Patterns and waves 18 (1986), 369-383, North-Holland, Amsterdam Zbl0623.35059MR882384
  3. C. Bardos, G. Lebeau, J. Rauch, Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary, SIAM J. Control Optim. 30 (1992), 1024-1065 Zbl0786.93009MR1178650
  4. N. Burq, P. Gérard, Condition nécessaire et suffisante pour la contrôlabilité exacte des ondes, C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), 749-752 Zbl0906.93008MR1483711
  5. J.-M. Coron, Control and nonlinearity, 136 (2007), American Mathematical Society, Providence, RI Zbl1140.93002MR2302744
  6. P. Degond, Local existence of solutions of the Vlasov-Maxwell equations and convergence to the Vlasov-Poisson equations for infinite light velocity, Math. Methods Appl. Sci. 8 (1986), 533-558 Zbl0619.35088MR870991
  7. S. Ervedoza, E. Zuazua, A systematic method for building smooth controls for smooth data, Discrete Contin. Dyn. Syst. Ser. B 14 (2010), 1375-1401 Zbl1219.93011MR2679646
  8. O. Glass, On the controllability of the Vlasov-Poisson system, J. Differential Equations 195 (2003), 332-379 Zbl1109.93007MR2016816
  9. O. Glass, LA MÉTHODE DU RETOUR EN CONTRoLABILITÉ ET SES APPLICATIONS EN MÉCANIQUE DES FLUIDES, Séminaire Bourbaki (2010) Zbl1302.93045
  10. O. Glass, D. Han-Kwan, On the controllability of the relativistic Vlasov-Maxwell system, Preprint (2012) Zbl06402810MR2902122
  11. O. Glass, D. Han-Kwan, On the controllability of the Vlasov-Poisson system in the presence of external force fields, J. Differential Equations 252 (2012), 5453-5491 Zbl1238.35160MR2902122
  12. R. Glassey, W. Strauss, Singularity formation in a collisionless plasma could occur only at high velocities, Arch. Rational Mech. Anal. 92 (1986), 59-90 Zbl0595.35072MR816621
  13. K. D. Phung, Contrôle et stabilisation d’ondes électromagnétiques, ESAIM Control Optim. Calc. Var. 5 (2000), 87-137 (electronic) Zbl0942.93002MR1744608
  14. J. Rauch, M. Taylor, Exponential decay of solutions to hyperbolic equations in bounded domains, Indiana Univ. Math. J. 24 (1974), 79-86 Zbl0281.35012MR361461
  15. J. Schaeffer, The classical limit of the relativistic Vlasov-Maxwell system, Comm. Math. Phys. 104 (1986), 403-421 Zbl0597.35109MR840744
  16. S. Wollman, An existence and uniqueness theorem for the Vlasov-Maxwell system, Comm. Pure Appl. Math. 37 (1984), 457-462 Zbl0592.45010MR745326
  17. S. Wollman, Local existence and uniqueness theory of the Vlasov-Maxwell system, J. Math. Anal. Appl. 127 (1987), 103-121 Zbl0645.35013MR904213

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