A two-level energy method for indirect boundary observability and controllability of weakly coupled hyperbolic systems

SIAM Journal on Control and Optimization

Volumn 42, Issue 3, 2003, Pages 871-906

  Alabau Boussouira, Fatiha ^a  

^a UNIVERSITÉ DE LORRAINE   (France)

Author keywords

Abstract linear evolution equations; Boundary observability; Hyperbolic systems; Indirect controllability

Indexed keywords

ABSTRACT LINEAR EVOLUTION EQUATION; BOUNDARY OBSERVABILITY; HYPERBOLIC SYSTEMS; INDIRECT CONTROLLABILITY;

DIFFERENTIAL EQUATIONS; FUNCTIONS; LINEAR SYSTEMS; MATHEMATICAL MODELS; PROBLEM SOLVING; VECTORS; WAVE EQUATIONS;

BOUNDARY CONDITIONS;

EID: 2942552471     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012902402608     Document Type: Article

References (31)

1. F. ALABAU-BOUSSOUIRA, Indirect boundary stabilization of weakly coupled hyperbolic systems, SIAM J. Control Optim., 41 (2002), pp. 511-541.
2. F. ALABAU AND V. KOMORNIK, Boundary observability, controllability, and stabilization of linear elastodynamic systems, SIAM J. Control Optim., 37 (1998), pp. 521-542.
3. F. ALABAU, Observabilité frontière indirecte de systèmes faiblement couplés, C. R. Acad. Sci. Paris Sér. I Math., 333 (2001), pp. 645-650.
4. F. ALABAU, P. CANNARSA, AND V. KOMORNIK, Indirect internal stabilization of weakly coupled systems, J. Evol. Equ., 2 (2002), pp. 127-150.
5. P. ALBANO AND D. TATARU, Carleman estimates and boundary observability for a coupled parabolic-hyperbolic system, Electron. J. Differential Equations, (2000), paper 22.
6. C. BARDOS, G. LEBEAU, AND J. RAUCH, Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary, SIAM J. Control Optim., 30 (1992), pp. 1024-1065.
7. A. BEYRATH, Indirect internal stabilization of coupled systems with locally distributed damping, C. R. Acad. Sci. Paris Sér I Math., 333 (2001), pp. 451-456.
8. N. BURQ AND G. LEBEAU, Mesures de défaut de compacité, application au systéme de Lamé, Ann. Sci. École Norm. Sup. (4), 34 (2001), pp. 817-870.
9. C. M. DAFERMOS, On the existence and the asymptotic stability of solutions to the equations of linear thermoelasticity, Arch. Ration. Mech. Anal., 29 (1968), pp. 241-271.
10. K.-J. ENGEL AND R. NAGEL, One-Parameter Semigroups for Linear Evolution Equations, Grad. Texts in Math. 194, Springer-Verlag, New York, 2000.
11. P. GRISVARD, Elliptic Problems in Nonsmooth Domains, Monogr. Stud. Math. 24, Pitman, Boston, 1985.
12. P. GRISVARD, Singularities in Boundary Value Problems, Rech. Math. Appl. 22, Masson, Paris, Springer-Verlag, Berlin, 1992.
13. P. GRISVARD, Contrôlabilité exacte des solutions de l'équation des ondes en présence de singularités, J. Math. Pures Appl., 68 (1989), pp. 215-259.
14. B. V. KAPITONOV, Uniform stabilization and exact controllability for a class of coupled hyperbolic systems, Comput. Appl. Math., 15 (1996), pp. 199-212.
15. B. V. KAPITONOV AND J. S. SOUZA, Observability and uniqueness theorem for a coupled hyperbolic system, Int. J. Math. Math. Sci., 24 (2000), pp. 423-432.
16. J. U. KIM AND Y. RENARDY, Boundary control of the Timoshenko beam, SIAM J. Control Optim., 25 (1987), pp. 1417-1429.
17. V. KOMORNIK, Exact Controllability and Stabilization. The Multiplier Method, RAM Res. Appl. Math. 36, Masson, Paris, John Wiley, Chicester, UK, 1994.
18. V. KOMORNIK AND P. LORETI, Ingham-type theorems for vector-valued functions and observability of coupled linear systems, SIAM J. Control Optim., 37 (1998), pp. 461-485.
19. V. KOMORNIK, Rapid boundary stabilization of linear distributed systems, SIAM J. Control Optim., 35 (1997), pp. 1591-1613.
20. V. KOMORNIK AND B. RAO, Boundary stabilization of compactly coupled wave equations, Asymptot. Anal., 14 (1997), pp. 339-359.
21. V. KOMORNIK AND E. ZUAZUA, A direct method for the boundary stabilization of the wave equation, J. Math. Pures Appl., 69 (1990), pp. 33-54.
22. J. E. LAGNESE AND J.-L. LIONS, Modelling Analysis and Control of Thin Plates, Rech. Math. Appl. 6, Masson, Paris, 1988.
23. I. LASIECKA, Uniform decay rates for full von Karman system of dynamic thermoelasticity with free boundary conditions and partial boundary dissipation, Comm. Partial Differerential Equations, 24 (1999), pp. 1801-1847.
24. I. LASIECKA AND R. TRIGGIANI, Carleman estimates and exact boundary controllability for a system of coupled, nonconservative second-order hyperbolic equations, in Partial Differential Equation Methods in Control and Shape Analysis, Lecture Notes in Pure and Appl. Math. 188, Dekker, New York, 1997, pp. 215-243.
25. J. L. LIONS, Contrôlabilité exacte et stabilisation de systèmes distribués, Vol. 1, Masson, Paris, 1988.
26. J. L. LIONS, Contrôlabilité exacte et stabilisation de systems distribués, Vol. 2, Masson, Paris, 1988.
27. K. LIU AND Z. LIU, Exponential stability and analyticity of abstract linear thermoelastic systems, Z. Angew. Math. Phys., 48 (1997), pp. 885-904.
28. A. PAZY, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, Springer-Verlag, New York, 1983.
29. J. E. MUNOZ RIVERA AND R. RACKE, Smoothing properties, decay, and global existence of solutions to nonlinear coupled systems of thermoelastic type, SIAM J. Math. Anal., 26 (1995), pp. 1547-1563.
30. D. L. RUSSELL, A general framework for the study of indirect damping mechanisms in elastic systems, J. Math. Anal. Appl., 173 (1993), pp. 339-358.
31. G. LEBEAU AND E. ZUAZUA, Decay rates for the three-dimensional linear system of thermoelasticity, Arch. Ration. Mech. Anal., 148 (1999), pp. 179-231.