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All issues Volume 27 (2021) ESAIM: COCV, 27 (2021) 98 References
Open Access
Issue
ESAIM: COCV
Volume 27, 2021
Article Number 98
Number of page(s) 25
DOI https://doi.org/10.1051/cocv/2021095
Published online 13 October 2021
  1. R.A. Adams and J.J.F. Fournier, Sobolev Spaces. Academic Press, Amsterdam, second edition (2003). [Google Scholar]
  2. B.T. Bilalov, Bases of exponentials, cosines, and sines formed by eigenfunctions of differential operators. Differ. Equ. 39 (2003) 652–657. [Google Scholar]
  3. A. Day, Heat Conduction within Linear Thermoelasticity. Springer-Verlag, New York (1985). [Google Scholar]
  4. B.Z. Guo and S.P. Yung, Asymptotic behavior of the eigenfrequency of a one-dimensional linear thermoelastic system. J. Math. Anal. Appl. 213 (1997) 406–421. [Google Scholar]
  5. B.Z. Guo, Further results for a one-dimensional linear thermoelastic equation with Dirichlet-Dirichlet boundary conditions. ANZIAM J. 43 (2002) 449–462. [Google Scholar]
  6. B.Z. Guo and J.C. Chen, The first real eigenvalue of a one-dimensional linear thermoelastic system. Comput. Math. Appl. 38 (1999) 249–256. [Google Scholar]
  7. B.Z. Guo, J.M. Wang and G.D. Zhang, Spectral analysis of a wave equation with Kelvin-Voigt damping. ZAMM Z. Angew. Math. Mech. 90 (2010) 323–342. [CrossRef] [MathSciNet] [Google Scholar]
  8. B.Z. Guo, Riesz basis approach to the stabilization of a flexible beam with a tip mass. SIAM J. Control Optim. 39 (2001) 1736–1747. [Google Scholar]
  9. B.Z. Guo and J.M. Wang, Control of Wave and Beam PDEs – The Riesz Basis Approach. Springer-Verlag, Cham (2019). [Google Scholar]
  10. B.Z. Guo and G.D. Zhang, On spectrum and Riesz basis property for one-dimensional wave equation with Boltzmann damping. ESAIM: COCV 18 (2012) 889–913. [CrossRef] [EDP Sciences] [Google Scholar]
  11. B.Z. Guo and K.Y. Chan, Riesz basis generation, eigenvalues distribution, and exponential stability for a Euler-Bernoulli beam with joint feedback control. Rev. Mat. Complut. 14 (2001) 205–229. [Google Scholar]
  12. B.Z. Guo, Riesz basis property and exponential stability of controlled Euler-Bernoulli beam equations with variable coefficients. SIAM J. Control Optim. 40 (2002) 1905–1923. [Google Scholar]
  13. Z.J. Han and G.Q. Xu, Spectral analysis and stability of thermoelastic Bresse system with second sound and boundary viscoelastic damping. Math. Methods Appl. Sci. 38 (2015) 94–112. [Google Scholar]
  14. T. Kato, Perturbation Theory for Linear Operators. Springer-Verlag, Berlin, second edition (1976). [Google Scholar]
  15. Z.H. Luo, B.Z. Guo and O. Morgül, Stability and Stabilization of Infinite-Dimensional Systems with Applications. Springer-Verlag, London (1999). [Google Scholar]
  16. K.S. Liu and Z.Y. Liu, Exponential stability and analyticity of abstract linear thermoelastic systems. Z. Angew. Math. Phys. 48 (1997) 885–904. [Google Scholar]
  17. Z.Y. Liu and S.M. Zheng, Exponential stability of the semigroup associated with a thermoelastic system. Quart. Appl. Math. 51 (1993) 535–545. [Google Scholar]
  18. M.A. Naimark, Linear Differential Operators, Part I: Elementary Theory of Linear Differential Operators. Frederick Ungar Publishing Co., New York (1967). [Google Scholar]
  19. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York (1983). [Google Scholar]
  20. M. Renardy, On the type of certain C0−semigroups. Comm. Partial Differ. Equ. 18 (1993) 1299–1307. [Google Scholar]
  21. M.A. Shubov, Asymptotic and spectral analysis of the spatially nonhomogeneous Timoshenko beam model. Math. Nachr. 241 (2002) 125–162. [Google Scholar]
  22. C. Tretter, Spectral problems for systems of differential equations y′ + A0y = λA1y with λ-polynomial boundary conditions. Math. Nachr. 214 (2000) 129–172. [Google Scholar]
  23. C. Tretter, Boundary eigenvalue problems for differential equations Nη = λPη and λ-polynomial boundary conditions. J. Differ. Equ. 170 (2001) 408–471. [Google Scholar]
  24. J.M. Wang, G.Q. Xu and S.P. Yung, Riesz basis property, exponential stability of variable coefficient Euler-Bernoulli beams with indefinite damping. IMA J. Appl. Math. 70 (2005) 459–477. [Google Scholar]
  25. J.M. Wang and B.Z. Guo, On dynamic behavior of a hyperbolic system derived from a thermoelastic equation with memory type. J. Franklin Inst. 344 (2007) 75–96. [Google Scholar]
  26. J.M. Wang, G.Q. Xu and S.P. Yung, Exponential stabilization of laminated beams with structural damping and boundary feedback controls. SIAM J. Control Optim. 44 (2005) 1575–1597. [Google Scholar]

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