Exact null controllability of structurally damped and thermo-elastic parabolic models

Irena Lasiecka; Roberto Triggiani

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1998)

  • Volume: 9, Issue: 1, page 43-69
  • ISSN: 1120-6330

Abstract

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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.

How to cite

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Lasiecka, Irena, and Triggiani, Roberto. "Exact null controllability of structurally damped and thermo-elastic parabolic models." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 9.1 (1998): 43-69. <http://eudml.org/doc/252346>.

@article{Lasiecka1998,
abstract = {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.},
author = {Lasiecka, Irena, Triggiani, Roberto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Exact null-controllability; Structurally damped parabolic equations; Thermo-elastic parabolic equations; parabolic models; structurally damped second-order equations; null controllability; distributed control; abstract thermoelastic equation; controlled mechanical systems},
language = {eng},
month = {3},
number = {1},
pages = {43-69},
publisher = {Accademia Nazionale dei Lincei},
title = {Exact null controllability of structurally damped and thermo-elastic parabolic models},
url = {http://eudml.org/doc/252346},
volume = {9},
year = {1998},
}

TY - JOUR
AU - Lasiecka, Irena
AU - Triggiani, Roberto
TI - Exact null controllability of structurally damped and thermo-elastic parabolic models
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1998/3//
PB - Accademia Nazionale dei Lincei
VL - 9
IS - 1
SP - 43
EP - 69
AB - 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.
LA - eng
KW - Exact null-controllability; Structurally damped parabolic equations; Thermo-elastic parabolic equations; parabolic models; structurally damped second-order equations; null controllability; distributed control; abstract thermoelastic equation; controlled mechanical systems
UR - http://eudml.org/doc/252346
ER -

References

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  1. Avdonin, S. A. - Ivanov, S. A., Families of Exponentials. The Method of Moments in Controllability Problems for Distributed Parameter Systems.Cambridge University Press, New York1995. Zbl0866.93001MR1366650
  2. Chen, G. - Russell, D. L., A mathematical model for linear elastic systems with structural damping. Quart. Appl. Math., 39, 1982, 433-454. Zbl0515.73033MR644099
  3. Chang, S. K. - Triggiani, R., 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. Zbl0911.35015MR1635994
  4. Chen, S. - Triggiani, R., Proof of two conjectures of G. Chen and D. L. Russell on structural damping for elastic systems: The case α = 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 York1988, 234-256. Zbl0669.34015MR996678DOI10.1007/BFb0089601
  5. Chen, S. - Triggiani, R., Proof of extensions of two conjectures on structural damping for elastic systems: The case 1 2 ≤ α ≤ 1 . Pacific J. Math., 39, 1989, 15-55. Zbl0633.47025MR971932
  6. Chen, S. - Triggiani, R., Characterization of domains of fractional powers of certain operators arising in elastic systems, and applications. J. Diff. Eqn., 88, 1980, 279-293. Zbl0717.34066MR1081250DOI10.1016/0022-0396(90)90100-4
  7. Hansen, S. - Zhang, B., Boundary control of a linear thermo-elastic beam. J. Math. Anal. & Appl., 20, 1997, 182-205. Zbl0873.73056MR1449516DOI10.1006/jmaa.1997.5437
  8. Triggiani, R., Regularity of some structurally damped problems with point control and with boundary control. J.M.A.A., 161, 1991, 299-331. Zbl0771.93013MR1132109DOI10.1016/0022-247X(91)90332-T
  9. Triggiani, R., Constructive steering control functions for linear systems and abstract rank conditions. J. Optimization Theory & Appl., 74, 1992, 347-367. Zbl0794.93056MR1170708DOI10.1007/BF00940899

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