Exact/approximate controllability of thermoelastic plates with variable thermal coefficients

Discrete and Continuous Dynamical Systems

Volumn 7, Issue 2, 2001, Pages 283-302

  Eller, M ^a   Lasiecka, I ^b   Triggiani, R ^b  

^a GEORGETOWN UNIVERSITY   (United States)

^b University of Virginia   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035625011     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2001.7.283     Document Type: Article

References (41)

1. P. Albano and D. Tataru, Carleman estimates and boundary observability for a coupled parabolic-hyperbolic system, Electronic J. of Diff. Eqns. 22 (2000), 1-15.
2. J. P. Aubin, Un théorèm de compacite. C. R. Acad. Sc. 256 (1963), 5042-5044.
3. G. Avalos, Exact controllability of a thermoelastic system with control in the thermal component only, Advances in Diff. Eqns., to appear.
4. G. Avalos and I. Lasiecka, Boundary controllability of thermo-elastic plates with free boundary conditions, SIAM J. Control, to appear.
5. C. Bardos, J. Lebeau, and J. Rauch, Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary, SIAM J. Control & Optimiz. 30 (1992), 1024-1065.
6. L. de Teresa and E. Zuazua, Controllability of the linear system of thermoelastic plates, Advances in Diff. Eqns. 1 (1996), 369-402.
7. M. Eller, Carleman estimates with a second large parameter, JMAA, to appear.
8. M. Eller, I. Lasiecka, and R. Triggiani, Simultaneous exact/approximate boundary controllability of thermoelastic plates with variable thermal coefficient, University of Virginia preprint, June 2000.
9. M. Eller, I. Lasiecka, and R. Triggiani, Unique continuation for over-determined Kirchoff plate equations and related thermoelastic systems, J. Inverse Ill-Posed Problems, to appear.
10. A. Fursikov and O. Imanuvilov, Controllability of Evolution Equations, Lecture Notes, Seoul National University, 1996.
11. S. W. Hansen and B. Zhang, Boundary control of a linear thermo-elastic beam, J. Math. Anal. & Appl. 210 (1997), 182-205.
12. V. Isakov, On the uniqueness of continuation for a thermoelasticity system, preprint, 1998.
13. B. Kellogg, Properties of solutions of elliptic boundary value problems, Chapter 3 in The Mathematical Foundations of the Finite Element Method with Applications to PDE, Ed. by A. K. Aziz, Academic Press, 1972.
14. V. Komornik, Exact controllability and stabilization, Masson, Paris, 1994.
15. J. Lagnese, Boundary Stabilization of Thin Plates, SIAM, Philadelphia, 1989.
16. J. Lagnese, The reachability problem for thermoelastic plates, Arch. Rational Mechanics and Analysis 112 (1990), 223-267.
17. J. Lagnese and J. .L. Lions, Modeling, Analysis and Control of Thin Plates, Masson, 1988.
18. I. Lasiecka, Controllability of viscoelastic Kirchoff plate, Inter. Series Numer. Math. 91 (1989), 237-247, Birkhäuser Verlag, Basel.
19. J. L. Lions, Controllabilite exacte, stabilization de systemes distribues, Vol. 1 and 2, Masson, Paris, 1988.
20. I. Lasiecka, J. L. Lions, and R. Triggiani, Nonhomogeneous boundary value problems for second order hyperbolic operators, J. Math. Pures et Appl. 65 (1986), 149-192.
21. I. Lasiecka, M. Renardy, and R. Triggiani, Backward uniqueness for thermoelastic plates with rotational forces, Semigroup Forum, to appear.
22. I. Lasiecka and R. Triggiani, Exact boundary controllability for the wave equations with Neumann boundary control, Appl. Math. & Optimiz. 19 (1989), 243-290. Preliminary version Springer Verlag LNCIS 100 (1987), 316-371.
23. I. Lasiecka and R. Triggiani, Exact boundary controllability for the wave equations with Neumann boundary control, Appl. Math. & Optimiz. 19 (1989), 243-290. Preliminary version Springer Verlag LNCIS 100 (1987), 316-371.
24. 2-boundary feedback in the Dirichlet B.C., J. Diff. Eqns. 66 (1987), 340-390.
25. I. Lasiecka and R. Triggiani, Exact controllability of semilinear abstract systems with application to waves and plates boundary control problems, Appl. Math. & Optimiz. 3 (1991), 109-154.
26. Σ, J. Diff. Eqns. 93 (1991), 62-101.
27. I. Lasiecka and R. Triggiani, Uniform boundary stabilization of the wave equation with Dirichlet and Neumann feedback control without geometric conditions, Appl. Math. Optimiz. 25 (1992), 189-224.
28. I. Lasiecka and R. Triggiani, Carleman's estimates and boundary controllability for a system of coupled, nonconservative second-order hyperbolic equations, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, Vol. 188, pp. 215-245, 1997.
29. I. Lasiecka and R. Triggiani, Structural decomposition of thermoelastic semigroups with rotational forces, Semigroup Forum 60(1) (2000), 16-66.
30. I. Lasiecka and R. Triggiani, Differential and Algebraic Riccati Equations with Applications to Boundary/Point Control Problems: Continuous Theory and Approximation Theory, LNCIS 164, Springer Verlag, 1991, pp. 160.
31. I. Lasiecka and R. Triggiani, Control for Partial Differential Equations: Continuous and Approximation Theories, Vols. I and II, Cambridge University Press, Encyclopedia of Mathematics and its Applications, January 2000.
32. I. Lasiecka and R. Triggiani, Exact null controllability of structurally damped and thermoelastic parabolic models, Atti Accademia Nazionale dei Lincei, Matematica e Applicazioni, Anno CCCXCV (1998), 43-69, Rome, Italy.
33. I. Lasiecka and R. Triggiani, Factor spaces and their implication on sharp regularity/exact controllability of Kirchoff elastic and thermoelastic systems with clamped boundary conditions, in progress.
34. -1 (Ω) for second order hyperbolic equations with variable coefficients, in Control of Distributed Parameter and Stochastic Systems, edited by S. Chen, X. Li, J. Yong, and X. Zhou, Kluwer Academic Publishers 1999, Proceedings of IFIP Conference held in Hangzhou, China, June 19-22, 1998.
35. I. Lasiecka, R. Triggiani, and P. F. Yao, Inverse/observability estimates for second order hyperbolic equations with variable coefficients, J. Math. Anal. & Appl. 235 (1999), 13-57. Preliminary announcement in "Non-Linear Analysis: Theory, Methods and Applications," 30 (1997), 111-122.
36. I. Lasiecka, R. Triggiani, and P. F. Yao, Inverse/observability estimates for second order hyperbolic equations with variable coefficients, J. Math. Anal. & Appl. 235 (1999), 13-57. Preliminary announcement in "Non-Linear Analysis: Theory, Methods and Applications," 30 (1997), 111-122.
37. D. Tataru, A priori estimates of Carleman's type in domains with boundaries, J. Math. Pures et Appl. 73 (1994), 355-387.
38. D. Tataru, A priori psuedo-convexity energy estimates in domains with boundary: Applications to exact boundary controllability for conservative PDE's, Ph.D. dissertation, University of Virginia, May 1992.
39. D. Tataru, Unique continuation for solutions to PDE's between Hörmander's theorem and Holmgren's theorem, Comm. Part. Diff. Eqn. 20 (1995), 855-884.
40. D. Tataru, Unique continuation for operators with partially analytic coefficients, J. Math. Pures Appl., 78 (1999), 505-521
41. R. Triggiani, Sharp regularity theory for thermo-elastic mixed problems, Applicable Analysis 73 (3-4) (1999), 557-572.