References
- Avalos G. The exponential stability of a coupled hyperbolic/parabolic system arising in structural acoustics. Abstr Appl Anal. 1996;1(2):203–217.
- Avalos G, Lasiecka I. Differential Riccati equation for the active control of a problem in structural acoustics.J Optim Theory Appl. 1996;91(3):695–728.
- Avalos G, Lasiecka I. Uniform decay rates of solutions to a structural acoustic model with nonlinear dissipation. Appl Math Comput Sci. 1998;8:287–312.
- Avalos G, Lasiecka I. Boundary controllability of thermoelastic plates via the free boundary conditions. SIAMJ Control Optim. 2000;38(2):337–383.
- Avalos G, Lasiecka I. Exact controllability of structural acoustic interactions. J Math Appl. 2003;82(8):1047–1073.
- Avalos G, Lasiecka I. Exact boundary controllability of a hybrid PDE system arising in structural acoustic modeling. In: Advances in dynamics and control. Nonlinear systems in aviation, aerospace, aeronautics, astronautics. Vol. 2. Boca Raton (FL): Chapman & Hall/CRC; 2004. p. 155–173.
- Avalos G, Lasiecka I. Exact reachability of finite energy states for an acoustic wave/plate interaction under the influence of boundary and localized controls. Adv Difference Equ. 2005;10(8):901–930.
- Avalos G, Lasiecka I, Rebarber R. Boundary controllability of a coupled wave/Kirchoff system. Syst Control Lett. 2003;50(5):326–341.
- Banks HT, Fang W, Silcox RJ, et al. Approximation methods for control of acoustic/structure models with piezoceramic actuators. NASA; 1991. (Contract Report 189578).
- Banks HT, Smith RC. Feedback control of noise in a 2D nonlinear structural acoustics model. Discrete Contin Dyn Syst. 1995;1:119–149.
- Beale JT. Spectral properties of an acoustic boundary condition. Indiana Univ Math J. 1976;25(9):895–917.
- Beale JT. Acoustic scattering from locally reacting surfaces. Indiana Univ Math J. 1977;26:199–222.
- Beale JT, Rosencrans SI. Acoustic boundary conditions. Bull Amer Math Soc. 1974;80:1276–1278.
- Gulliver R, Lasiecka I, Littman W, et al. The case for differential geometry in the control of single and coupled PDEs: the structural acoustic chamber. In: Geometric methods in inverse problems and PDE control. New York (NY): Springer-Verlag; 2004. p. 73–181. (IMA Vol. Math. Appl.; vol. 137).
- Liu B, Littman W. On the spectral properties and stabilization of acoustic flow. SIAM J Appl Math. 1998;59(1):7–34.
- Mores PM, Ingard KU. Theoretical acoustics. Princeton (NJ): Princeton University Press; 1968.
- Li J, Chai S. Stabilization of the variable-coefficient structural acoustic model with curved middle surface and delay effects in the structural component. J Math Anal Appl. 2017;454(2):510–532.
- Liu Y, Bin-Mohsin B, Hajaiej H, et al. Exact controllability of structural acoustic interactions with variable coefficients. SIAM J Control Optim. 2016;54(4):2132–2153.
- Yang F, Yao P, Chen G. Boundary controllability of structural acoustic systems with variable coefficients and curved walls. Math Control Signals Syst. 2018;30(1):5.
- Bucci F. Control–theoretic properties of structural acoustic models with thermal effects. J Evol Equ. 2007;7(3):387–414.
- Dalsen GV. On a structural acoustic model which incorporates shear and thermal effects in the structural component. J Math Anal Appl. 2008;341(2):1253–1270.
- Yao PF. On the observability inequalities for the exact controllability of the wave equation with variable coefficients. SIAM J Control Optim. 1999;37(5):1568–1599.
- Cavalcanti MM, Khemmoudj A, Medjden M. Uniform stabilization of the damped Cauchy-Ventcel problem with variable coefficients and dynamic boundary conditions. J Math Anal Appl. 2007;328(2):900–930.
- Chai S, Guo BZ. Well-posedness and regularity of Naghdi's shell equation under boundary control and observation. J Differ Equ. 2010;249(2):3174–3214.
- Chai S, Guo Y, Yao PF. Boundary feedback stabilization of shallow shells. SIAM J Control Optim. 2003;42(1):239–259.
- Chai S, Liu K. Boundary feedback stabilization of the transmission problem of Naghdis model. J Math Anal Appl. 2006;319(1):199–214.
- Feng SJ, Feng DX. Nonlinear internal damping of wave equations with variable coefficients. Acta Math Sin. 2004;20(6):1057–1072.
- Guo BZ, Shao ZC. On exponential stability of a semilinear wave equation with variable coefficients under the nonlinear boundary feedback. Nonlinear Anal. 2009;71(12):5961–5978.
- Guo Y, Yao PF. On boundary stability of wave equations with variable coefficients. Acta Math Appl Sin. 2002;18(4):589–598.
- Lasiecka I, Triggiani R, Yao PF. Inverse/observability estimates for second-order hyperbolic equations with variable coefficients. J Math Anal Appl. 1999;235(1):13–57.
- Li J, Chai S. Energy decay for a nonlinear wave equation of variable coefficients with acoustic boundary conditions and a time-varying delay in the boundary feedback. Nonlinear Anal. 2015;112:105–117.
- Liu Y. Exact controllability of the wave equation with time-dependent and variable coefficients. Nonlinear Anal Real World Appl. 2019;45:226–238.
- Lu L, Li S, Chen G, et al. Control and stabilization for the wave equation with variable coefficients in domains with moving boundary. Syst Control Lett. 2015;80:30–41.
- Nicaise S, Pignotti C. Stabilization of the wave equation with variable coefficients and boundary condition of memory type. Asymptot Anal. 2006;50(1–2):31–67.
- Yao PF. Observability inequalities for shallow shells. SIAM J Control Optim. 2000;38(6):1729–1756.
- Yao PF. Observability inequalities for the Euler–Bernoulli plate with variable coefficients, differential geometric methods in the control of partial differential equations. Contemp Math. 2000;268:383–406.
- Yao PF. Global smooth solutions for the quasilinear wave equation with boundary dissipation. J Differ Equ. 2007;241(1):62–93.
- Yao PF. Boundary controllability for the quasilinear wave equation. Appl Math Optim. 2010;61:191–233.
- Yao PF. Modeling and control in vibrational and structural dynamics. A differential geometric approach. Boca Raton (FL): CRC Press; 2011.
- Wu H, Shen CL, Yu YL. An introduction to Riemannian geometry (in Chinese). Beijing: Beijing University Press; 1989.
- Avalos G, Lasiecka I. Exact-approximate boundary reachability of thermoelastic plates under variable thermal coupling. Inverse Probl. 2000;16:979–996.
- Dolecki S, Russell DL. A general theory of observation and control. SIAM J Control Optim. 1977;15:185–220.
- Miyatake S. Mixed problems for hyperbolic equations. J Math Kyoto Univ. 1973;130:435–487.
- Lasiecka I, Triggiani R. Recent advances in regularity of second-order hyperbolic mixed problems, and applications. Dyn Rep Expos Dyn Syst. 1994;3:104–158.
- Lasiecka I, Triggiani R. Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions. Appl Math Optim. 1992;25(2):189–224.
- Simon J. Compact sets in the space Lp(0,T;B). Ann Mat Appl. 1986;146(1):65–96.
- Hörmander L. Linear partial differential operators. New York (NY): Springer–Verlag; 1969.