Free Access
Issue
ESAIM: COCV
Volume 18, Number 3, July-September 2012
Page(s) 889 - 913
DOI https://doi.org/10.1051/cocv/2011186
Published online 27 September 2011
  1. G. Amendola, M. Fabrizio, J.M. Golden and B. Lazzari, Free energies and asymptotic behaviour for incompressible viscoelastic fluids. Appl. Anal. 88 (2009) 789–805. [CrossRef] [MathSciNet]
  2. H.T. Banks, G.A. Pinter, L.K. Potter, B.C. Munoz and L.C. Yanyo, Estimation and control related issues in smart material structures and fluids, The 4th International Conference on Optimization: Techniques and Applications. Perth, Australia (1998) 19–34.
  3. H.T. Banks, J.B. Hood and N.G. Medhin, A molecular based model for polymer viscoelasticity: intra- and inter-molecular variability. Appl. Math. Model. 32 (2008) 2753–2767. [CrossRef] [MathSciNet]
  4. G. Chen, S.A. Fulling, F.J. Narcowich and S. Sun, Exponential decay of energy of evolution equations with locally distributed damping. SIAM J. Control Optim. 51 (1991) 266–301.
  5. S.P. Chen, K.S. Liu and Z.Y. Liu, Spectrum and stability for elastic systems with global or local Kelvin-Voigt damping. SIAM J. Appl. Math. 59 (1999) 651–668. [MathSciNet]
  6. C.M. Dafermos, An abstract Volterra equation with application to linear viscoelasticity. J. Differential Equations 7 (1970) 554–569. [CrossRef] [MathSciNet]
  7. M. Fabrizio and B. Lazzari, On the existence and asymptotic stability of solutions for linearly viscoelastic solids. Arch. Ration. Mech. Anal. 116 (1991) 139–152. [CrossRef]
  8. M. Fabrizio and S. Polidoro, Asymptotic decay for some diferential systems with fading memory. Appl. Anal. 81 (2002) 1245–1264. [CrossRef] [MathSciNet]
  9. I.C. Gohberg and M.G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators, Trans. Math. Monographs 18. AMS Providence (1969).
  10. 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. [CrossRef] [MathSciNet]
  11. 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. [CrossRef] [MathSciNet]
  12. B.Z. Guo and H. Zwart, Riesz Spectral System. Preprint, University of Twenty, the Netherlands (2001).
  13. B.Z. Guo, J.M. Wang and G.D. Zhang, Spectral analysis of a wave equation with Kelvin–Voigt damping. Z. Angew. Math. Mech. 90 (2010) 323–342. [CrossRef] [MathSciNet]
  14. B. Jacob, C. Trunk and M. Winklmeier, Analyticity and Riesz basis property of semigroups associated to damped vibrations. J. Evol. Equ. 8 (2008) 263–281. [CrossRef] [MathSciNet]
  15. K.S. Liu and Z.Y. Liu, On the type of C0-semigroup associated with the abstract linear viscoelastic system. Z. Angew. Math. Phys. 47 (1996) 1–15. [CrossRef] [MathSciNet]
  16. K.S. Liu and Z.Y. Liu, Exponential decay of energy of the Euler–Bernoulli beam with locally distributed Kelvin–Voigt damping. SIAM J. Control Optim. 36 (1998) 1086–1098. [CrossRef] [MathSciNet]
  17. K.S. Liu and Z.Y. Liu, Exponential decay of energy of vibrating strings with local viscoelasticity. Z. Angew. Math. Phys. 53 (2002) 265–280. [CrossRef] [MathSciNet]
  18. Y.Z. Liu and S.M. Zheng, On the exponential stability of linear viscoelasticity and thermoviscoelasticity. Quart. Appl. Math. 54 (1996) 21–31. [MathSciNet]
  19. B.P. Rao, Optimal energy decay rate in a damped Rayleigh beam, Contemporary Mathematics. RI, Providence 209 (1997) 221–229.
  20. M. Renardy, On localized Kelvin–Voigt damping. Z. Angew. Math. Mech. 84 (2004) 280–283. [CrossRef] [MathSciNet]
  21. J.E.M. Rivera and H.P. Oquendo, The transmission problem of viscoelastic waves. Acta Appl. Math. 62 (2000) 1–21. [CrossRef] [MathSciNet]
  22. H.S. Tzou and J.H. Ding, Optimal control of precision paraboloidal shell structronic systems. J. Sound Vib. 276 (2004) 273–291. [CrossRef]
  23. J.M. Wang, B.Z. Guo and M.Y. Fu, Dynamic behavior of a heat equation with memory. Math. Methods Appl. Sci. 32 (2009) 1287–1310. [CrossRef] [MathSciNet]
  24. H.L. Zhao, K.S. Liu and Z.Y. Liu, A note on the exponential decay of energy of a Euler–Bernoulli beam with local viscoelasticity. J. Elasticity 74 (2004) 175–183. [CrossRef] [MathSciNet]
  25. H.L. Zhao, K.S. Liu and C.G. Zhang, Stability for the Timoshenko beam system with local Kelvin-Voigt damping. Acta Math. Sinica (Engl. Ser.) 21 (2005) 655–666. [CrossRef] [MathSciNet]
  26. E. Zuazua, Exponential decay for the semilinear wave equation with locally distributed damping. Comm. Partial Differential Equations 15 (1990) 205–235. [CrossRef] [MathSciNet]

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.