Contrôle et stabilisation d'ondes électromagnétiques

Kim Dang Phung

ESAIM: Control, Optimisation and Calculus of Variations (2000)

  • Volume: 5, page 87-137
  • ISSN: 1292-8119

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Dang Phung, Kim. "Contrôle et stabilisation d'ondes électromagnétiques." ESAIM: Control, Optimisation and Calculus of Variations 5 (2000): 87-137. <http://eudml.org/doc/90586>.

@article{DangPhung2000,
author = {Dang Phung, Kim},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {exact controllability; Maxwell equation; boundary controllability; internal controllability; HUM method; boundary stabilization},
language = {fre},
pages = {87-137},
publisher = {EDP Sciences},
title = {Contrôle et stabilisation d'ondes électromagnétiques},
url = {http://eudml.org/doc/90586},
volume = {5},
year = {2000},
}

TY - JOUR
AU - Dang Phung, Kim
TI - Contrôle et stabilisation d'ondes électromagnétiques
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2000
PB - EDP Sciences
VL - 5
SP - 87
EP - 137
LA - fre
KW - exact controllability; Maxwell equation; boundary controllability; internal controllability; HUM method; boundary stabilization
UR - http://eudml.org/doc/90586
ER -

References

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  1. [1] H. Barucq, Étude asymptotique du système de Maxwell avec conditions aux limites absorbantes. Thèse de l'université de Bordeaux I ( 1993). 
  2. [2] N. Burq, Mesures semi-classiques et mesures de défaut, Séminaire Bourbaki. Asterisque 245 ( 1997) 167-195. Zbl0954.35102MR1627111
  3. [3] H. Barucq et B. Hanouzet, Étude asymptotique du système de Maxwell avec la condition aux limites absorbante de Silver-Müller II. C. R. Acad. Sci. Paris Sér. I Math. 316 ( 1993) 1019-1024. Zbl0776.35073MR1222965
  4. [4] C. Bardos, L. Halpern, G. Lebeau, J. Rauch et E. Zuazua, Stabilisation de l'équation des ondes au moyen d'un feedback portant sur la condition aux limites de Dirichlet. Asymptot. Anal. 4 ( 1991) 285-291. Zbl0764.35055MR1127003
  5. [5] C. Bardos, G. Lebeau et 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
  6. [6] M. Cessenat, Mathematical method in electromagnetism - linear theorie and applications. Ser. Adv. Math. Appl. Sci. 41 ( 1996). Zbl0917.65099MR1409140
  7. [7] R. Dautray et J.-L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques. Masson ( 1988). Zbl0642.35001
  8. [8] V. Komornik, Boundary stabilization, observation and control of Maxwell's equations. Panamer. Math. J. 4 ( 1994) 47-61. Zbl0849.35136MR1310321
  9. [9] J. Lagnese, Exact boundary controllability of Maxwell's equations in a general region. SIAM J. Control Optim. 27 ( 1989) 374-388. Zbl0678.49032MR984833
  10. [10] G. Lebeau, Contrôle et stabilisation hyperboliques. Séminaire E.D.P. École Polytechnique ( 1990). Zbl0706.35004MR1073191
  11. [11] J.-L. Lions, Contrôlabilité exacte, stabilisation et perturbation des systèmes distribués. RMA, Masson, Paris ( 1988). Zbl0653.93002MR953547
  12. [12] J.-L. Lions et E. Magenes, Problèmes aux limites non homogènes. Dunod ( 1968). 
  13. [13] G. Lebeau et L. Robbiano, Stabilisation de l'équation des ondes par le bord. Duke Math. J. 86 ( 1997) 465-491. Zbl0884.58093MR1432305
  14. [14] R. Melrose et J. Sjöstrand, Singularities of boundary value problems I. Comm. Pure Appl. Math. 31 ( 1978) 593-617. Zbl0368.35020MR492794
  15. [15] R. Melrose et J. Sjöstrand, Singularities of boundary value problems II. Comm. Pure Appl. Math. 35 ( 1982) 129-168. Zbl0546.35083MR644020
  16. [16] O. Nalin, Contrôlabilité exacte sur une partie du bord des équations de Maxwell. C. R. Acad. Sci. Paris Sér. I Math. 309 ( 1989) 811-815. Zbl0688.49041MR1055200
  17. [17] A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer-Verlag, New York ( 1983). Zbl0516.47023MR710486
  18. [18] K.-D. Phung, Stabilisation frontière du système de Maxwell avec la condition aux limites absorbante de Silver-Müller. C. R. Acad. Sci. Paris Sér. I Math. 3233 ( 1995) 187-192. Zbl0844.35125MR1320353
  19. [19] K.-D. Phung, Contrôlabilité exacte et stabilisation interne des équations de Maxwell. C. R. Acad. Sci. Paris Sér. I Math. 3233 ( 1996) 169-174. Zbl0858.93011MR1402537
  20. [20] J.V. Ralston, Solutions of Wave equation with localized energy. Comm. Pure. Appl. Math. 22 ( 1969) 807-823. Zbl0209.40402MR254433
  21. [21] J. Rauch et M. Taylor, Penetration into shadow region and unique continuation properties in hyperbolic mixed problems. Indiana Univ. Mathematics J. 22 ( 1972) 277-284. Zbl0227.35064MR303098
  22. [22] M. Taylor, Pseudodifferential operators, Princeton Univ. Press, Princeton, N.J. ( 1981). Zbl0453.47026MR618463
  23. [23] M. Taylor, Reflection of singularities of solutions to systems of differential equations. Comm. Pure Appl. Math. 28 ( 1975) 457-478. Zbl0332.35058MR509098
  24. [24] M. Taylor, Grazing rays and reflection of singularities of solutions to wave equations II. Comm. Pure Appl. Math. 29 ( 1976) 463-481. Zbl0335.35059MR427839
  25. [25] N. Week, Exact boundary controllability for a Maxwell problem, submitted to SIAM J. Control. Optim. Zbl0963.93040
  26. [26] N. Weck et K.J. Witsch, Low frequency asymptotics for dissipative Maxwell's equations in bounded domains. Math. Methods Appl. Sci. 13 ( 1990) 81-93. Zbl0704.35007MR1060225
  27. [27] K. Yamamoto, Singularities of solutions to the boundary value problem for elastic and Maxwell's equations. Japan J. Math. (N.S.) 14 ( 1988) 119-163. Zbl0669.73017MR945621

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