Open Access
Volume 27, 2021
Article Number 98
Number of page(s) 25
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 = 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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.