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Stabilisation d'un modèle d'interaction fluide-structure
Kais Ammari
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 10 (2001) no. 2, p. 225-254
@article{AFST_2001_6_10_2_225_0,
     author = {Ammari, Kais},
     title = {Stabilisation d'un mod\`ele d'interaction fluide-structure},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier},
     address = {Toulouse},
     volume = {6e s{\'e}rie, 10},
     number = {2},
     year = {2001},
     pages = {225-254},
     mrnumber = {1896180},
     zbl = {01796093},
     language = {fr},
     url = {https://afst.centre-mersenne.org/item/AFST_2001_6_10_2_225_0}
}
Ammari, Kais. Stabilisation d'un modèle d'interaction fluide-structure. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 10 (2001) no. 2, pp. 225-254. afst.centre-mersenne.org/item/AFST_2001_6_10_2_225_0/

[1] Allibert (B.) and Micu (S.) . - Controllability of analytic functioncs for a wave equation coupled with a beam, Rev. Mat. Iberoamericana., 15 (1999), 547-592. | MR 1742216 | Zbl 0946.35045

[2] Ammari (K.). - Stabilisation d'une classe d'équations d'évolution du deuxième ordre en temps, Thèse de doctorat de l'École Polytechnique, 2000.

[3] Ammari (K.) and Tucsnak (M.). - Stabilization of second order evolution equations by a class of unbounded feedbacks, ESAIM Control Optim. Calc. Var, à paraître. | Numdam | MR 1836048 | Zbl 0992.93039

[4] Ammari (K.) and Tucsnak (M.). - Stabilization of Bernoulli-Euler beams by means of a pointwise feedback force, SIAM J. Control. Optim., 39 (2000), 1160-1181. | MR 1814271 | Zbl 0983.35021

[5] Avalos (G.), Lasiecka (I.) and Rebarber (R.). - Lack of time-delay robustness for stabilization of a structural acoustics model, SIAM. J. Control. Optim., 37 (2000), 1394-1418. | MR 1710226 | Zbl 0947.93020

[6] Avalos (G.) and Lasiecka (I.). - A differential Riccati equation for the active control of a problem in structural acoustics, J. Optim. Theory Appl. 91 (1996), 695-728. | MR 1419861 | Zbl 0869.93023

[7] Banks (H.T.), Fang (W.), Silox (R.J.) and Smith (R.C.). - Approximation methods for control of acoustic/structure models with piezoceramic actuators, Journal of intelligent Material systems and Structures., 4 (1993), 98-116.

[8] Bardos (C.), Lebeau (G.) and Rauch (J.). - Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary, SIAM J. Control Optim., 30 (1992), 1024-1065. | MR 1178650 | Zbl 0786.93009

[9] Bensoussan (A.), Da Prato (G.), Delfour (M.) and Mitter (S.). Representation and Control of Infinite Dimensional Systems, vol. 1, Birkhäuser, Boston, 1992. | MR 1182557 | Zbl 0781.93002

[10] Dafermos (C.). - Asymptotic behavior of solutions of evolution equations in "Nonlinear evolution equations" (M.G. Crandall, Ed.), 103-123, Academic Press, New York, 1978. | MR 513814 | Zbl 0499.35015

[11] Doetsch (G.). - Introduction to the theory and application of the Laplace transformation, Springer, Berlin, 1974. | MR 344810 | Zbl 0278.44001

[12] Grisvard (P.). - Caratérisation de quelques espaces d'interpolation, Arch. Rational. Mech. Anal., 25 (1967), 40-63. | MR 213864 | Zbl 0187.05901

[13] Haraux (A.). - Quelques propriétés des séries lacunaires utiles dans l'étude des systèmes élastiques, Nonlinear partial differential equations and their applications. Collège de France Seminar, Vol. XII (Paris, 1991-1993), 113-124, Pitman Res. Notes Math. Ser., 302, Longman Sci. Tech., Harlow, 1994. | MR 1291847 | Zbl 0805.35070

[14] Haraux (A.) and Jaffard (S.). - Pointwise and spectral control of plate vibrations, Rev. Mat. Iberoamericana, 7 (1997), 1-23. | MR 1109478 | Zbl 0778.73045

[15] Ingham (A.E.). - Some trigonometrical inequalities with applications in the theory of series, Math. Z., 41 (1936), 367-369. | JFM 62.0225.01 | Zbl 0014.21503

[16] Katznelson (Y.). - An introduction to harmonic analysis, Dover, New York, 1968. | Zbl 0169.17902

[17] Lasiecka (I.) and Triggiani (R.). - Control theory for partial differential equations : continuous and approximation theories. II. Abstract hyperbolic-like systems over a finite time horizon. Encyclopedia of Mathematics and its Applications, 75. Cambridge University Press, Cambridge, 2000. | Zbl 0961.93003

[18] Lions (J.L.) et Magenes (E.). - Problèmes aux limites non homogènes et applications, Dunod, Paris, 1968. | Zbl 0165.10801

[19] Rebarber (R.). - Exponential stability of beams with dissipative joints : a frequency domain approach, SIAM. J. Control. Optim., 33 (1995), 1-28. | MR 1311658 | Zbl 0819.93042

[20] Russell (D.L.). - Decay rates for weakly damped systems in Hilbert space obtained with control theoretic methods, J. Diff. Eq., 19 (1975), 344-370. | MR 425291 | Zbl 0326.93018

[21] Weiss (G.). - Transfer functions of regular linear systems, part I: charaterization of regularity, Trans. Amer. Math. Soc. 342 (1994), 827-854. | MR 1179402 | Zbl 0798.93036