Optimal estimates of norms of fast controls in exact null controllability of two non-classical abstract parabolic systems

Advances in Differential Equations

Volumn 8, Issue 2, 2003, Pages 189-229

  Triggiani, R ^a  

^a University of Virginia   (United States)

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EID: 7444261910     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. G. Avalos and I. Lasiecka, A note on the null controllability of thermoelastic plates and singularity of the associated minimal energy function, preprint, June 2002.
2. G. Avalos and I. Lasiecka, Optimal blow-up rates for the minimal energy null control for the structurally damped abstract wave equation, preprint, July 2002.
3. D. Aze and O. Carja, Fast controls and minimum time, Contr. & Cyber., 29, N4 (2000), 887-894.
4. A. Benabdallah and M. G. Naso, Null controllability of a thermoelastic plate, preprint 2001.
5. G. Chen and D. Russell, A mathematical model for linear elastic systems with structural damping, Quant. Appl. Math., 39 (1982), 433-454.
6. S. Chen and R. Triggiani, Proof of two conjectures of G. Chen and D. Russel 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 York 1988, 234-256.
7. S. Chen and R. Triggiani, 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.
8. S. Chen and R. Triggiani, Characterization of domains of fractional powers of certain operators arising in elastic systems, J. Diff. Eqns., 88 (1990), 279-293.
9. S. Chen and R. Triggiani, Gevrey class semigroups arising from elastic systems: the case 0 < a < 1 2, Proc. Amer. Math. Soc., 220 (1990), 401-415.
10. H. B. Dwight, "Tables of Integrals and Other Mathematical Data," MacMillan, 1957.
11. I. Lasiecka and R. Triggiani, Exact null controllability of structurally damped and thermoelastic parabolic models, Atti della Accademia Nazionale dei Lincei, Mathematica e Applicasioni (1998), Serie IX, volume IX.
12. I. Lasiecka and R. Triggiani, Exact controllability of the wave equation with Neumann boundary control, AMO, 19 (1989), 243-290.
13. I. Lasiecka and R. Triggiani, "Control Theory for Partial Differential Equations: Continuous and Approximation Theories," Vol. 1, Cambridge University Press, January 2000.
14. R. Triggiani, Controllability and observability in Banach space with bounded operators, SIAM J. Control, 13 (1975), 462-491.
15. R. Triggiani, Constructive steering control functions for linear systems and abstract rank conditions, J. Opt. Th. & Appl., 74, (1992), 347-367.
16. R. Triggiani, Regularity of some structurally damped problems with point control and with boundary control, JMAA, 161 (1991), 299-331.
17. T. Seidman, How violent are fast controls? Math. Control, Signals, Syst., 1 (1988), 89-95.
18. T. Seidman and J. Yong, How violent are fast controls?, II, Math. Control, Signals, Syst., 9 (1997), 327-340.