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Volumn 78, Issue 2, 1999, Pages 203-232

Boundary stabilization of a 3-dimensional structural acoustic model (1)

Author keywords

Nonlinear dissipation; Plate equation; Structural acoustic model; Trace estimates; Uniform decay rates; Wave equation

Indexed keywords


EID: 0033074721     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-7824(01)80009-X     Document Type: Article
Times cited : (52)

References (45)
  • 1
    • 0000276432 scopus 로고    scopus 로고
    • The exponential stability of a coupled hyperbolic/parabolic system arising in structural acoustic
    • G. Avalos, The exponential stability of a coupled hyperbolic/parabolic system arising in structural acoustic, Abstract and Applied Analysis, 1, 1996, pp. 203-218.
    • (1996) Abstract and Applied Analysis , vol.1 , pp. 203-218
    • Avalos, G.1
  • 2
    • 0000026765 scopus 로고    scopus 로고
    • The strong stability of a semigroup arising from a coupled hyperbolic/parabolic system
    • G. Avalos and I. Lasiecka, The strong stability of a semigroup arising from a coupled hyperbolic/parabolic system, Semigroup Forum, 1998.
    • (1998) Semigroup Forum
    • Avalos, G.1    Lasiecka, I.2
  • 3
    • 0009303180 scopus 로고    scopus 로고
    • Uniform decay rates of solutions to a structural acoustic model with nonlinear dissipation
    • G. Avalos and I. Lasiecka, Uniform decay rates of solutions to a structural acoustic model with nonlinear dissipation, Applied Mathematics and Computer Science, 8, No 2, 1998, pp. 101-121.
    • (1998) Applied Mathematics and Computer Science , vol.8 , Issue.2 , pp. 101-121
    • Avalos, G.1    Lasiecka, I.2
  • 4
    • 0009228924 scopus 로고
    • Active control of acoustic pressure fields using smart material technology in flow control
    • M. Gunzburger, Springer Verlag
    • H. T. Banks and R. Smith, Active control of acoustic pressure fields using smart material technology in flow control. In M. Gunzburger, IMA, 68. Springer Verlag, 1995.
    • (1995) IMA , vol.68
    • Banks, H.T.1    Smith, R.2
  • 5
    • 0026923885 scopus 로고
    • Sharp sufficient conditions for the observation,control and stabilization of waves from the boundary
    • C. Bardos and G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation,control and stabilization of waves from the boundary, Siam J. Control, 30, 1992, pp. 1024-1065.
    • (1992) Siam J. Control , vol.30 , pp. 1024-1065
    • Bardos, C.1    Lebeau, G.2    Rauch, J.3
  • 6
    • 0031274516 scopus 로고    scopus 로고
    • Dynamic boundary control of beams using active constrained layer damping
    • A. Baz, Dynamic boundary control of beams using active constrained layer damping. Mechanical Syastems and Signal Processing, 11, 1997, pp. 811-825.
    • (1997) Mechanical Syastems and Signal Processing , vol.11 , pp. 811-825
    • Baz, A.1
  • 7
    • 0016998564 scopus 로고
    • Spectral properties of an acoustic boundary condition
    • J. Beale, Spectral properties of an acoustic boundary condition, Indiana Univ. Math. J., 9, 1976, pp. 895-917.
    • (1976) Indiana Univ. Math. J. , vol.9 , pp. 895-917
    • Beale, J.1
  • 9
    • 84972562987 scopus 로고
    • Proof of extensions of two conjectures on structural damping for elastic systems
    • S. Chen and R. Triggiani, Proof of extensions of two conjectures on structural damping for elastic systems, Pacific J. of Mathematics, 136(1), 1989, pp. 15-55.
    • (1989) Pacific J. of Mathematics , vol.136 , Issue.1 , pp. 15-55
    • Chen, S.1    Triggiani, R.2
  • 10
    • 0023437632 scopus 로고
    • Use of piezoelectric actuators as elements of intelligent structures
    • October
    • E.F. Crawley and J. de Luis, Use of piezoelectric actuators as elements of intelligent structures, AIAA Journal, 25, October 1987, pp. 1373-1385.
    • (1987) AIAA Journal , vol.25 , pp. 1373-1385
    • Crawley, E.F.1    De Luis, J.2
  • 12
    • 85030062633 scopus 로고    scopus 로고
    • A new model for acoustic interaction and its exponential stability
    • to appear
    • F. Fahroo and C. Wang, A new model for acoustic interaction and its exponential stability, Quaterly of Applied Mathematics, to appear.
    • Quaterly of Applied Mathematics
    • Fahroo, F.1    Wang, C.2
  • 16
    • 0000943951 scopus 로고
    • Exact controllability and uniform stabilization of the Kirchhoff plate equation with boundary feedback acting via bending moments
    • M.A. Horn, Exact controllability and uniform stabilization of the Kirchhoff plate equation with boundary feedback acting via bending moments. J. Math. Anal. Applic., 167, 1992, pp. 557-581.
    • (1992) J. Math. Anal. Applic. , vol.167 , pp. 557-581
    • Horn, M.A.1
  • 17
    • 84972498136 scopus 로고
    • Uniform decay of weak solutions to a von Karman plate with nonlinear dissipation
    • M.A. Horn and I. Lasiecka, Uniform decay of weak solutions to a von Karman plate with nonlinear dissipation, Differential and Integral Equations, 7, 1994, pp. 7885-7908.
    • (1994) Differential and Integral Equations , vol.7 , pp. 7885-7908
    • Horn, M.A.1    Lasiecka, I.2
  • 18
    • 38249000245 scopus 로고
    • Carlemans type estimates in anisotropic case and applications
    • V. Isakov, Carlemans type estimates in anisotropic case and applications. J. Differential Equations, 105, 1993, pp. 217-238.
    • (1993) J. Differential Equations , vol.105 , pp. 217-238
    • Isakov, V.1
  • 23
    • 0003280914 scopus 로고
    • Boundary stabilization of thin plates
    • Philadelphia
    • J. Lagnese, Boundary stabilization of thin plates. SIAM, Philadelphia, 1989.
    • (1989) SIAM
    • Lagnese, J.1
  • 25
    • 38249014043 scopus 로고
    • Exponential decay rates for the solutions of Euler-Bernoulli equations with boundary dissipation occurring in the moments only
    • I. Lasiecka, Exponential decay rates for the solutions of Euler-Bernoulli equations with boundary dissipation occurring in the moments only. J. Differential Eq., 95, 1992, pp. 169-182.
    • (1992) J. Differential Eq. , vol.95 , pp. 169-182
    • Lasiecka, I.1
  • 26
    • 33751542104 scopus 로고
    • Existence and uniqueness of the solutions to second order abstract equations with nonlinear and non-monotone boundary conditions
    • I. Lasiecka, Existence and uniqueness of the solutions to second order abstract equations with nonlinear and non-monotone boundary conditions, J. Nonlinear Analysis, Methods and Applications, 23, 1994, pp. 797-823.
    • (1994) J. Nonlinear Analysis, Methods and Applications , vol.23 , pp. 797-823
    • Lasiecka, I.1
  • 27
    • 0032338703 scopus 로고    scopus 로고
    • Mathematical control theory in structural acoustic problems
    • I. Lasiecka, Mathematical control theory in structural acoustic problems, Mathematical Methods in Applied Sciences, 8/7, 1998.
    • (1998) Mathematical Methods in Applied Sciences , vol.8 , Issue.7
    • Lasiecka, I.1
  • 28
    • 0032123713 scopus 로고    scopus 로고
    • Riccati equations arising in acoustic structure interactions with curved walls
    • I. Lasiecka and R. Marchand, Riccati equations arising in acoustic structure interactions with curved walls, Dynamics and Control 8, 1998, pp. 269-292.
    • (1998) Dynamics and Control , vol.8 , pp. 269-292
    • Lasiecka, I.1    Marchand, R.2
  • 29
    • 84972506618 scopus 로고
    • Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping
    • I. Lasiecka and D. Tataru, Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping. Differential and Integral Equations, 6, 1993, pp. 507-533.
    • (1993) Differential and Integral Equations , vol.6 , pp. 507-533
    • Lasiecka, I.1    Tataru, D.2
  • 30
    • 0001450314 scopus 로고
    • Sharp regularity results for mixed second order hyperbolic equations of neumann type. Part II: General boundary data
    • I. Lasiecka and R. Triggiani, Sharp regularity results for mixed second order hyperbolic equations of neumann type. Part II: General boundary data. J. Diff Eq., 94, 1991, pp. 112-164.
    • (1991) J. Diff Eq. , vol.94 , pp. 112-164
    • Lasiecka, I.1    Triggiani, R.2
  • 31
    • 0026838533 scopus 로고
    • Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometric conditions
    • I. Lasiecka and R. Triggiani, Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometric conditions, Applied Math. Optimiz., 25, 1992, pp. 189-224.
    • (1992) Applied Math. Optimiz. , vol.25 , pp. 189-224
    • Lasiecka, I.1    Triggiani, R.2
  • 32
    • 0000988025 scopus 로고
    • Sharp trace estimates of solutions to Kirchhoff and Euler-Bernoulli equations
    • I. Lasiecka and R. Triogiani, Sharp trace estimates of solutions to Kirchhoff and Euler-Bernoulli equations. Applied Math. Optimiz., 28, 1993, pp. 277-306.
    • (1993) Applied Math. Optimiz. , vol.28 , pp. 277-306
    • Lasiecka, I.1    Triogiani, R.2
  • 33
    • 0000910737 scopus 로고
    • Recent advances in regularity of second-order hyperbolic mixed problems, and applications
    • I. Lasiecka and R. Triggiani, Recent advances in regularity of second-order hyperbolic mixed problems, and applications. In Dynamics Reported- Expositions in Dynamical Systems, 3, 1994, pp. 25-104.
    • (1994) Dynamics Reported- Expositions in Dynamical Systems , vol.3 , pp. 25-104
    • Lasiecka, I.1    Triggiani, R.2
  • 34
    • 85003264565 scopus 로고
    • Active control of propeller induced noise fields inside a flexible cylinder
    • Seattle, WA
    • H.C. Lester and C.R. Fuller, Active control of propeller induced noise fields inside a flexible cylinder. In Proc. of AIAA Tenth Aeroacoustics Conference, Seattle, WA, 1986.
    • (1986) Proc. of AIAA Tenth Aeroacoustics Conference
    • Lester, H.C.1    Fuller, C.R.2
  • 35
    • 0009229988 scopus 로고    scopus 로고
    • On the spectral properties and stabilization of acoustic flow
    • W. Littman and B. Liu, On the spectral properties and stabilization of acoustic flow. IMA Preprint, 1436, 1997.
    • (1997) IMA Preprint , vol.1436
    • Littman, W.1    Liu, B.2
  • 36
    • 0002616259 scopus 로고
    • Stabilization of hybrid system of elasticity by feedback boundary damping
    • W. Littman and L. Markus, Stabilization of hybrid system of elasticity by feedback boundary damping, Annali di Mathematica Pura et Applicata, 152, 1988, pp. 281-330.
    • (1988) Annali di Mathematica Pura et Applicata , vol.152 , pp. 281-330
    • Littman, W.1    Markus, L.2
  • 37
    • 0009228665 scopus 로고    scopus 로고
    • Boundary stabilization of nonhomogenous beam by frequency domain multiplier method
    • K. Liu and Z. Liu, Boundary stabilization of nonhomogenous beam by frequency domain multiplier method. Preprint, 1997.
    • (1997) Preprint
    • Liu, K.1    Liu, Z.2
  • 38
    • 85030074758 scopus 로고    scopus 로고
    • Boundary controllability of a linear hybrid system arising in the control of noise
    • to appear
    • S. Micu and E. Zuazua, Boundary controllability of a linear hybrid system arising in the control of noise, SIAM J. Control, to appear.
    • SIAM J. Control
    • Micu, S.1    Zuazua, E.2
  • 40
    • 0001559853 scopus 로고
    • Mixed problems for hyperbolic equations
    • S. Myatake, Mixed problems for hyperbolic equations. J. Math. Kyoto Univ. 130, 1973, pp. 435-487.
    • (1973) J. Math. Kyoto Univ. , vol.130 , pp. 435-487
    • Myatake, S.1
  • 41
    • 0000820706 scopus 로고
    • Controllability and stabilizability theory for linear partial differential equations. recent progress and open questions
    • D.L. Russell, Controllability and stabilizability theory for linear partial differential equations. recent progress and open questions. SIAM Review, 20, 1978, pp. 639-739.
    • (1978) SIAM Review , vol.20 , pp. 639-739
    • Russell, D.L.1
  • 42
    • 0001674328 scopus 로고
    • Mathematical models for the elastic beam and their control-theoretic properties
    • D.L. Russell, Mathematical models for the elastic beam and their control-theoretic properties. Semigroups Theory and Applications, Pitman Research Notes, 152, 1986, pp. 177-217.
    • (1986) Semigroups Theory and Applications, Pitman Research Notes , vol.152 , pp. 177-217
    • Russell, D.L.1
  • 43
    • 0000983021 scopus 로고
    • A priori estimates of carleman's type in domains with boundary
    • D. Tataru, A priori estimates of carleman's type in domains with boundary, J. Math. Pures Appi., 73. 1994. pp. 355-387.
    • (1994) J. Math. Pures Appi. , vol.73 , pp. 355-387
    • Tataru, D.1


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