Geodesic
Exact null controllability of structurally damped and thermo-elastic parabolic models
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 1, pp. 43-69.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We show exact null-controllability for two models of non-classical, parabolic partial differential equations with distributed control: (i) second-order structurally damped equations, except for a limit case, where exact null controllability fails; and (ii) thermo-elastic equations with hinged boundary conditions. In both cases, the problem is solved by duality.
In questa Nota dimostriamo la proprietà di controllabilità esatta all’origine per due modelli di equazioni alle derivate parziali, di tipo parabolico, non-classiche, con controllo distribuito: (i) equazioni del secondo ordine fortemente smorzate, eccetto che per un caso limite dove tale proprietà di controllabilità è falsa; (ii) equazioni termo-elastiche, con condizioni al contorno incernierate. In entrambi i casi, il problema è risolto per dualità. 
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Lasiecka, Irena; Triggiani, Roberto. Exact null controllability of structurally damped and thermo-elastic parabolic models. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 1, pp. 43-69. http://geodesic.mathdoc.fr/item/RLIN_1998_9_9_1_a4/

[1] S. A. Avdonin - S. A. Ivanov, Families of Exponentials. The Method of Moments in Controllability Problems for Distributed Parameter Systems. Cambridge University Press, New York 1995. | MR | Zbl

[2] G. Chen - D. L. Russell, A mathematical model for linear elastic systems with structural damping. Quart. Appl. Math., 39, 1982, 433-454. | MR | Zbl

[3] S. K. Chang - R. Triggiani, Spectral Analysis of Thermo-elastic Plates with Rotational Forces. Proceedings of IFIP Workshop on Control, held at University of Florida, Gainesville, February 1997, Kluwer, to appear. | MR | Zbl

[4] S. Chen - R. Triggiani, Proof of two conjectures of G. Chen and D. L. Russell on structural damping for elastic systems: The case \( \alpha = \frac{1}{2} \). Proceedings of the International Seminar on Approximation and Optimization (University of Havana, Cuba, Jan. 12-16, 1987). Lecture notes in mathematics, vol. 1354, Springer-Verlag, Berlin-New York 1988, 234-256. | DOI | MR | Zbl

[5] S. Chen - R. Triggiani, Proof of extensions of two conjectures on structural damping for elastic systems: The case \( \frac{1}{2} \le \alpha \le 1 \). Pacific J. Math., 39, 1989, 15-55. | fulltext mini-dml | MR | Zbl

[6] S. Chen - R. Triggiani, Characterization of domains of fractional powers of certain operators arising in elastic systems, and applications. J. Diff. Eqn., 88, 1980, 279-293. | DOI | MR | Zbl

[7] S. Hansen - B. Zhang, Boundary control of a linear thermo-elastic beam. J. Math. Anal. & Appl., 20, 1997, 182-205. | DOI | MR | Zbl

[8] R. Triggiani, Regularity of some structurally damped problems with point control and with boundary control. J.M.A.A., 161, 1991, 299-331. | DOI | MR | Zbl

[9] R. Triggiani, Constructive steering control functions for linear systems and abstract rank conditions. J. Optimization Theory & Appl., 74, 1992, 347-367. | DOI | MR | Zbl