Backward uniqueness for thermoelastic plates with rotational forces

Semigroup Forum

Volumn 62, Issue 2, 2001, Pages 217-242

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

^a University of Virginia   (United States)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041469987     PISSN: 00371912     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002330010035     Document Type: Article

References (29)

1. Avalos, G. and I. Lasiecka, Boundary controllability of thermoelastic plates with free B.C., SIAM J. Control & Optimiz. 38 (2000), 337-383.
2. Brenner, S. and L. R. Scott, "The Mathematical Theory of Finite Elements Methods", Texts in Applied Mathematics 15, Springer-Verlag, New York, 1994.
3. Bardos, C. and L. Tartar, Sur l'unicité retrograde des equations paraboliques et quelques questions voisines, Arch. Rat. Mech. Anal. 50 (1973), 10-25.
4. Bensoussan, A., G. DaPrato, M. Delfour and S. Mitter, "Representation and Control of Infinite Dimensional Systems", Vol. 1, Birkhäuser, Boston, Basel, Berlin, 1992.
5. Chang, S. K. and R. Triggiani, Spectral analysis of thermoelastic plates with rotational forces, in "Optimal Control: Theory, Algorithms, and Applications", W. W. Hager & P. M. Pardalos, eds., Kluwer, 1998, 84-115.
6. Conway, J., "Functions of One Complex Variable", 2nd ed., Springer-Verlag, 1978.
7. Eller, M., Uniqueness of continuation theorems, "Proceedings of the ISAAC Conference", 1997 Direct and Inverse Problems of Mathematical Physics, Kluwer Academic, Dordrecht, Boston, London, 1999, 53-105.
8. Eller, M., I. Lasiecka and R. Triggiani, Simultaneous exact/approximate boundary controllability of thermo-elastic plates with variable transmission coefficient, Lecture Notes in Pure & Applied Mathematics, Marcel Dekker, New York, J. Cagnol, M. Polis, J. P. Zolesio, Editors, to appear.
9. Eller, M., I. Lasiecka and R. Triggiani, Unique continuation for over-determined Kirchhoff plate equations and related thermoelastic systems, J. Inverse & Ill-Posed Problems, to appear.
10. Grisvard, P., Characterisation de qualques espaces d'interpolation, Arch. Rational Mech. & Anal. 25 (1967), 40-63.
11. Hille, E. and R. Phillips, "Functional Analysis and Semigroups", AMS Colloquium Publications, American Mathematical Society, Providence, RI, Vol. XXXI, 1957.
12. Isakov, V., "Inverse Problems for Partial Differential Equations", Springer-Verlag, New York, 1998.
13. Isakov, V., On the uniqueness of the continuation for a thermo-elastic system, preprint 1998.
14. Lagnese, J., "Uniform Boundary Stabilization of Homogeneous Isotropic Plates", Springer-Verlag LNCIS 102 (1987), New York, 204-215.
15. Lagnese, J., "Boundary Stabilization of Thin Plates", SIAM, Philadelphia, 1989.
16. Lagnese, J. and J. L. Lions, "Modeling, Analysis, and Control of Thin Plates", Masson, Paris, 1988.
17. Lasiecka, I. and R. Triggiani, Two direct proofs of analyticity of the strongly continuous semigroup arising in abstract thermo-elastic equations, Advances in Diff. Eqns. 3(3) (1998), 387-416.
18. Lasiecka, I. and R. Triggiani, Analyticity of thermo-elastic semigroups with hinged/Neumann B.C., Abstract and Applied Analysis 3(1-2) (1998), 153-169.
19. Lasiecka, I. and R. Triggiani, Analyticity of thermo-elastic semigroups with free B.C., "Annali Scuola Normale Superiore", Pisa, Cl. Sc. (4), vol. XXVII (1998).
20. Lasiecka, I. and R. Triggiani, Structural decomposition of thermoelastic semigroups with rotational forces, Semigroup Forum 60(1) (2000), 16-66.
21. Lasiecka, I. and R. Triggiani, "Control Theory for Partial Differential Equations: Continuous and Approximation Theories", Vol. I, Cambridge University Press, Encyclopedia of Mathematics and its Applications, 680 pp., 2000.
22. Lions, J. L., "Optimal Control of Systems Governed by Partial Differential Equations", Springer-Verlag, New York, 1970.
23. Lions, J. L. and B. Malgrange, Sur l'unicité retrograde dans les problemes mixtes paraboliques, Math. Scand. 8 (1960), 277-286.
24. Lions, J. L. and E. Magenes, "Nonhomogeneous Boundary Value Problems and Applications", Vol. I, Springer-Verlag, New York, 1972.
25. Liu, Z. and M. Renardy, A note on equations of a thermoelastic plate, Appl. Math. Letters 8 (1995), 1-6.
26. Mizohata, S., Unicité du prolongement des solutions pour quelques operateurs differentials parabolique, Mém. Coll. Sc. Univ. Kyoto (Serie A) 31 (1958), 219-239.
27. Pazy, A., "Semigroups of Linear Operators and Applications to Partial Differential Equations", Springer-Verlag, New York, 1983.
28. Thomee, V., "Galerkin Finite Element Methods for Parabolic Problems", Lecture Notes in Mathematics, Vol. 1054, Springer-Verlag 1984; Expanded version reported as a Springer-Verlag book, New York, 1997.
29. Titchmarsh, E. C., "The Theory of Functions", 2nd ed., Oxford University Press, 1939.