Exact controllability of finite energy states for an acoustic wave/plate interaction under the influence of boundary and localized controls

Advances in Differential Equations

Volumn 10, Issue 8, 2005, Pages 901-930

  Avalos, George ^a   Lasiecka, Irena ^b  

^a UNIVERSITY OF NEBRASKA LINCOLN   (United States)

^b University of Virginia   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34248138000     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (49)

1. B. Allibert and S. Micu, Controllability of analytic functions for a wave equation coupled with a beam, Revista Matemática Iberoamericana, 15 (1999), 547-592.
2. G. Avalos, Sharp regularity estimates for solutions to wave equations and their traces with prescribed Neumann data, Appl. Math. Optim., 35 (1997), 203-221.
3. G. Avalos, The exponential stability of a coupled hyerbolic/parabolic system arising in structural acoustics, Appl. Abstr. Anal., 1, 203-217.
4. G. Avalos and I. Lasiecka, Exact-approximate boundary reachability of thermoelastic plates under variable thermal coupling, Inverse Problems, 16 (2000), 979-996.
5. G. Avalos and I. Lasiecka, Differential Riccati equation for the active control of a problem in structural acoustics, J. Optim. Theory Appl., 91 (1996), 695-728.
6. G. Avalos and I. Lasiecka, The strong stability of a semigroup arising from a coupled hyperbolic/parabolic system, Semigroup Forum, 57 (1998), 278-292.
7. G. Avalos and I. Lasiecka, Boundary controllability of thermoelastic plates via the free boundary conditions, SIAM J. Control Optim., 38 (2000), 337-383.
8. G. Avalos, I. Lasiecka, and R. Rebarber, Well-posedness of a structural acoustics control model with point observation of the pressure, Journal of Differential Equations, 173 (2001), 40-78.
9. G. Avalos, I. Lasiecka, and R. Rebarber, Boundary controllability of a coupled wave/Kirchoffsystem, Systems and Control Letters, 50 (2003), 331-341.
10. G. Avalos and I. Lasiecka, Exact controllability of structural acoustic interactions, J. Math. Pures Appl., 82 (2003), 1047-1073.
11. H.T. Banks, W. Fang, R.J. Silcox, R. Smith, Approximation methods for control of acoustic/structure models with piezoceramic actuators, Contract Report, 189578 NASA (1991).
12. V. Barbu, "Nonlinear Semigroups and Differential Equations in Banach Spaces," Nordhoff, 1976.
13. 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), 1024-1065.
14. J. T. Beale, Spectral properties of an acoustic boundary condition, Indiana Univ. Math. J., 25 (1976), 895-917.
15. J. Cagnol and C. Lebiedzik, Optimal control of a structural acoustic model with flexible curved walls, Control and Boundary Analysis, Lecture Notes in Pure and Applied Mathematics (239), Marcel Dekker, New York (1995), 37-52.
16. M. Camurdan and R. Triggiani, Sharp regularity of a coupled system of a wave and a Kirchoffplate with point control arising in noise reduction, Differential and Integral Equations, 12 (1999), 101-107.
17. P. Grisvard, Characterization de quelques espaces d'interpolation, Arch. Rational Mech. Anal., 25 (1967), 40-63.
18. M. Grobbelaar-Van Dalsen, On a structural acoustic model with interface a Reissner-Mindlin plate or a Timishenko beam, Preprint (2004).
19. L. Hörmander, "The Analysis of Linear Partial Differential Operators I," Springer-Verlag, New York, 1983.
20. M.S. Howe, "Acoustics of Fluid-Structure Interaction," Cambridge University Press (1998).
21. M. Eller, Carleman estimates with a second large parameter, JMAA, 249 (2000), 491-514.
22. R. Gulliver and W. Littman, Chord uniquenes and controllability, the view from the boundary, Contemporary Mathematics, AMS, 268 (2000), 145-175.
23. V. Komornik, "Exact Controllability-Multipliers Method," Masson.
24. J. Lagnese, Decay of solutions of wave equation in a bounded region with boundary dissipation, J. Differential Equations, 50 (1983), 106-113.
25. I. Lasiecka, "Mathematical Control Theory of Coupled PDE's," CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM Publishing, Philadelphia (2002).
26. I. Lasiecka, Boundary stabilization of a three-dimensional structural acoustic model, Journal of Mathematiques Pures et Applique, 78 (1999), 203-322.
27. I. Lasiecka, J.L. Lions, and R. Triggiani, Nonhomogeneous boundary value problems for second order operators, J. Math. Pures et Appl., 65 (1986), 149-192.
28. I. Lasiecka and R. Triggiani, Exact controllability of the wave equation with Neumann boundary control, Appl. Math. Optim., 19 (1989), 243-290.
29. 2 boundary data, Ann, di Math. Pura Appl. (Ser. 4), CLVII (1990), 285-367.
30. I. Lasiecka and R. Triggiani, Regularity theory of hyperbolic equations with nonhomogenous Neumann boundary conditions: General boundary data, J, Diff. Equations, 94 (1991), 112-164.
31. I. Lasiecka and R. Triggiani, Exact controllability and uniform stabilization of Kirchoffplates woth boundary control only on δw|∑ and homogeneous boundary displacement, Journal of Differential Equations, 93 (1991), 62-101.
32. I. Lasiecka and R. Triggiani, Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control with no geometrical conditions, Appl. Math. Optim., 25 (1992), 189-224.
33. J. L. Lions and E. Magenes, "Nonhomogeneous Boundary-Value Problems and Applications," Springer-Verlag, Berlin, Germany (1972).
34. W. Littman and B. Liu, On the spectral properties and stabilization of acoustic flow, IMA, University of Minnesota, IMA Preprint Series #1436, (November, 1996).
35. W. Littman and S. Markus, Stabilization of hybrid system of elasticity by feedback boundary damping, Annali di Mathematica Pura et Applicata, 152 (1988), 281-330.
36. R. Gulliver and I. Lasiecka, W. Littman, and R. Triggiani, "Geometric Methods in Inverse Problems and PDE Control," vol 137, Springer Verlag (2000).
37. S. Micu and E. Zuazua, Boundary controllability of a linear hybrid system arising in the control of noise, SIAM J. Control Optim., 35 (1997), 531-555.
38. S. Miyatake, Mixed problems for hyperbolic equations, J. Math. Kyoto Univ., 130 (1973), 435-487.
39. C.S. Morawetz, Energy identities for the wave equation, NYU Courant Institute, Math. Sci. Res. Rep. No. IMM 346 (1976).
40. P.M. Morse and K. U. Ingard, "Theoretical Acoustics," McGraw-Hill, New York (1968).
41. D.L. Russell, Controllability and stabilizability theory for linear partial differential equations, recent progress and open questions, SIAM Rev., 20 (1978), 639-739.
42. W. Strauss, Dispersal of waves vanishing on the boundary of an exterior domain, Comm. Pure Appl. Mat., 28 (1976), 265-278.
43. I. Lasiecka and R. Triggiani, Recent advances in regularity of second-order hyperbolic mixed problems, and applications, Dynamics Reported: Expositions in Dynamical Systems, 3 (1994), 104-158.
44. J. Simon, Compact sets in the space Lp(0, T;B), Ann. Mat. Pura Appl., (4) 148 (1987), 65-96.
45. D. Tataru, On the regularity of boundary traces for the wave equation, Annali Scuola Normale di Pisa, Classe Scienze (4), 26 (1998), 185-206.
46. D. Tataru A priori estimates of Carleman's type in domains with boundary, Journal de Mathematiques Pure et Appliques, 73 (1994), 355-387.
47. M. Taylor, "Pseudodifferential Operators," Princeton University Press, Princeton, NJ (1981).
48. R. Triggiani, Wave equation on a bounded domain with boundary dissipation: an operator approach, Journal of Mathematical Analysis and Applications, 137 (1989), 438-461.
49. P. Yao. Observability inequalities for shallow shells, Siam J. Control, 38 (2000), 1729-1758.