Exact controllability of shells in minimal time
Loreti, Paola
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 12 (2001), p. 43-48 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)

We prove an exact controllability result for thin cups using the Fourier method and recent improvements of Ingham type theorems, given in a previous paper [2].

Dimostriamo un risultato di controllabilità esatta per calotte sottili, utilizzando il metodo di Fourier e miglioramenti recenti di teoremi di tipo Ingham, dati in un precedente articolo [2].

Publié le : 2001-03-01
@article{RLIN_2001_9_12_1_43_0,
     author = {Paola Loreti},
     title = {Exact controllability of shells in minimal time},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {12},
     year = {2001},
     pages = {43-48},
     zbl = {1170.93310},
     mrnumber = {1898447},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_2001_9_12_1_43_0}
}

Loreti, Paola. Exact controllability of shells in minimal time. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 12 (2001) pp. 43-48. http://gdmltest.u-ga.fr/item/RLIN_2001_9_12_1_43_0/

[1] Baiocchi, C. - Komornik, V. - Loreti, P., Ingham type theorems and applications to control theory. Boll. Un. Mat. Ital., B (8), II - B, n. 1 febbraio 1999, 33-63. | MR 1794544 | Zbl 0924.42022

[2] Baiocchi, C. - Komornik, V. - Loreti, P., Généralisation d’un théorème de Beurling et application à la théorie du contrȏle. C. R. Acad. Sci. Paris Sér. I Math., 330 (4), 2000, 281-286. | MR 1753294 | Zbl 0964.42019

[3] Carleson, L. - Malliavin, P. - Neuberger, J. - Wermer, J., The Collected Works of Arne Beurling. Vol. 2, Birkhäuser, Boston 1989.

[4] Geymonat, G. - Loreti, P. - Valente, V., Introduzione alla controllabilità esatta per la calotta sferica. Quaderno IAC 8/1989.

[5] Geymonat, G. - Loreti, P. - Valente, V., Exact Controllability of a shallow shell model. Int. Series of Num. Math., 107, 1992, 85-97. | MR 1223361 | Zbl 0766.73044

[6] Geymonat, G. - Loreti, P. - Valente, V., Exact controllability of a spherical shell via harmonic analysis. In: J.-L. Lions - C. Baiocchi (eds.), Boundary Values Problems for Partial Differential Equations and Applications. Masson, Paris 1993. | MR 1260466 | Zbl 0803.73052

[7] Geymonat, G. - Loreti, P. - Valente, V., Spectral problems for thin shells and exact controllability. In: Spectral Analysis of Complex Structures. Travaux en cours, 49, Hermann, Paris 1995, 35-57. | MR 1488734 | Zbl 0840.35112

[8] Ingham, A. E., Some trigonometrical inequalities with applications in the theory of series. Math. Z., 41, 1936, 367-379. | MR 1545625 | Zbl 0014.21503

[9] Jaffard, S. - Tucsnak, M. - Zuazua, E., On a theorem of Ingham. J. Fourier Anal. Appl., 3, 1997, n. 5, 577-582. | MR 1491935 | Zbl 0939.42004

[10] Komornik, V. - Loreti, P., Ingham type theorems for vector-valued functions and observability of coupled linear systems. SIAM J. Control Optim., 37, 1998, 461-485. | MR 1655862 | Zbl 0963.93013

[11] Komornik, V. - Loreti, P., Observability of compactly perturbed systems. J. Math. Anal. Appl., 243, 2000, 409-428. | MR 1741532 | Zbl 0952.34047

[12] Lagnese, J., Boundary Stabilization of Thin Plates. SIAMStudies in Appl. Math., Philadelphia1989. | MR 1061153 | Zbl 0696.73034

[13] Lagnese, J. - Lions, J.-L., Modelling, Analysis and Control of Thin Plates. Masson, Paris 1988. | MR 953313 | Zbl 0662.73039

[14] Lions, J.-L., Exact controllability, stabilization and perturbations for distributed systems. SIAM J. Control Optim., 30, 1988, 1-68. | MR 931277 | Zbl 0644.49028

[15] Lions, J.-L., Contrôlabilité exacte et stabilisation de systèmes distribués. Voll. 1-2, Masson, Paris1988. | Zbl 0653.93002

[16] Loreti, P., Application of a new Ingham type theorem to the control of spherical shells. In: V. Zakharov (ed.), Proceedings of the 11th IFAC International Workshop Control Applications of Optimization (St. Petersburg, Russia, July 3-6, 2000). Pergamon, 2000.

[17] Love, A. E. H., A treatise on the mathematical theory of elasticity. Dover, New York1944. | JFM 47.0750.09 | MR 10851 | Zbl 0063.03651

[18] Sanchez, E., Asymptotic and spectral properties of a class of singular-stiff problems. J. Math. Pures Appl., 71, 1992, 379-406. | MR 1191581 | Zbl 0833.47011

[19] Timoshenko, S., Theory of elastic stability. McGraw-Hill, New York1936. | MR 134026

[20] Titchmarsh, E. C., Eigenfunction Expansions Associated with Second-Order Differential Equations. Clarendon Press, Oxford1962. | MR 176151 | Zbl 0099.05201