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All issues Volume 31 (2025) ESAIM: COCV, 31 (2025) 63 References
Open Access
Issue
ESAIM: COCV
Volume 31, 2025
Article Number 63
Number of page(s) 26
DOI https://doi.org/10.1051/cocv/2025049
Published online 28 July 2025
  1. K.A. Morris and A.Ö. Özer, Strong stabilization of piezoelectric beams with magnetic effects. IEEE Conf. Decis. Control (2013) 3014-3019. [Google Scholar]
  2. K.A. Morris and A.Ö. Özer, Modeling and stabilizability of voltage-actuated piezoelectric beams with magnetic effects. SIAM J. Control Optim. 52 (2014) 2371–2398. [CrossRef] [MathSciNet] [Google Scholar]
  3. K.A. Morris and A.Ö. Özer, Comparison of stabilization of current-actuated and voltage-actuated piezoelectric beams. IEEE Conf. Decis. Control (2014) 571-576. [Google Scholar]
  4. H.E Zhang, G.Q. Xu and Z.J. Han, Stability and eigenvalue asymptotics of multi-dimensional fully magnetic effected piezoelectric system with friction-type infinite memory. SIAM J. Appl. Math. 83 (2023) 510–529. [Google Scholar]
  5. M.J. Dos Santos, J.C.P. Fortes and M.L. Cardoso, Exponential stability for a piezoelectric beam with a magnetic effect and past history. Discrete Continuous Dyn. Syst. Ser. B 27 (2022) 5487–5501. [Google Scholar]
  6. A.J.A. Ramos, M.M. Freitas, D.S. Almeida Júnior, S.S. Jesus and T.R.S. Moura, Equivalence between exponential stabilization and boundary observability for piezoelectric beams with magnetic effect. Z. Angew. Math. Phys. 70 (2019) Article number 60. [Google Scholar]
  7. H.E Zhang, G.Q. Xu and Z.J. Han, Stability of multi-dimensional nonlinear piezoelectric beam with viscoelastic infinite memory. Z. Angew. Math. Phys. 73 (2022) Article number 159. [Google Scholar]
  8. C.M. Dafermos, Asymptotic stability in viscoelasticity. Arch. Rational Mech. Anal. 37 (1970) 297–308. [Google Scholar]
  9. V. Volterra, Sur la théorie mathématique des phénomènes héréditaires. J. Math. Pures Appl. 7 (1928) 249–298. [Google Scholar]
  10. H.S. Tzou and J.H. Ding, Optimal control of precision paraboloidal shell structronic systems. J. Sound Vib. 276 (2004) 273–291. [Google Scholar]
  11. B.Z. Guo and G.D. Zhang, On spectrum and Riesz basis property for one-dimensional wave equation with Boltzmann dmping. ESAIM: Control, Optimization and Calculus of Variations 18 (2012) 889–913. [Google Scholar]
  12. G.Q. Xu, Resolvent family for the evolution process with memory. Math. Nachr. 296 (2023) 2626–2656. DOI: 10.1002/mana.202100203. [Google Scholar]
  13. B.Z. Guo and J.M. Wang, Control of Wave and Beam PDEs: The Riesz Basis Approach. Communications and Control Engineering, Springer Nature Switzerland AG, Switzerland (2019). [Google Scholar]
  14. M.M. Cavalcanti, V.N. Cavalcanti and T.F. Ma, Exponential decay of the viscoelastic Euler–Bernoulli equation with a nonlocal dissipation in general domains. Differ. Integral Equ. 17 (2004) 495–510. [Google Scholar]
  15. M. Fabrizio and S. Polidoro, Asymptotic decay for some differential systems with fading memory. Appl. Anal. 81 (2002) 1245–1264. [Google Scholar]
  16. B.Z. Guo, J.M. Wang and M.Y. Fu, Dynamic behavior of a heat equation with memory. Math. Meth. Appl. Sci. 32 (2009) 1287–1310. [Google Scholar]
  17. 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. [Google Scholar]
  18. 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 [Google Scholar]
  19. J.E.M. Rivera and H.P. Oquendo, The transmission problem of viscoelastic waves. Acta Appl. Math. 62 (2000) 1–21. [Google Scholar]
  20. J. Wang and J.M. Wang, Spectral analysis and exponential stability of one-dimensional wave equation with viscoelastic damping. J. Math. Anal. Appl. 410 (2014) 499–512. [Google Scholar]
  21. Z.F. Yang, Existence and energy decay of solutions for the Euler–Bernoulli viscoelastic equation with a delay. Z. Angew. Math. Phys. 66 (2015) 727–745. [Google Scholar]
  22. M. Astudillo and H.P. Oquendo, Stability results for a Timoshenko system with a fractional operator in the memory. Appl. Math. Optim. 83 (2021) 1247–1275. [Google Scholar]
  23. J.E.M. Rivera and H.D.F. Sare, Stability of Timoshenko systems with past history. J. Math. Anal. Appl. 339 (2008) 482–502. [Google Scholar]
  24. L. Gearhart, Spectral theory for contraction semigroups on Hibert space. Trans. Amer. Math. Soc. 236 (1978) 385–394. [CrossRef] [MathSciNet] [Google Scholar]
  25. F.L. Huang, Characteristic conditions for exponential stability of linear dynamical systems in Hilbert spaces. Ann. Differ. Equ. 1 (1985) 43–56. [Google Scholar]
  26. Z.Y. Liu and S. Zheng, Semigroups associated with dissipative systems. Res. Notes Math., Vol. 398. Chapman & Hall/CRC, Boca Raton (1999). [Google Scholar]
  27. J. Pruss, On the spectrum of C0-semigroups. Trans. Amer. Math. Soc. 284 (1984) 847–857. [Google Scholar]
  28. C. Giorgi and F.M. Vegni, Uniform energy estimates for a semilinear evolution equation of the Mindlin–Timoshenko beam with memory. Math. Comput. Model. 39 (2004) 1005–1021. [Google Scholar]
  29. A. Guesmia, Asymptotic behavior for coupled abstract evolution equations with one infinite memory. Appl. Anal. 94 (2015) 184–217. [Google Scholar]
  30. M.J. Dos Santos, M.M. Freitas, A.Ö. Özer, A.J.A. Ramos and D.S. Almeida Junior, Global attractors for a novel nonlinear piezoelectric beam model with dynamic electromagnetic effects and viscoelastic memory. Z. Angew. Math. Phys. 73 (2022) Article number 136. [Google Scholar]
  31. G. Liu, A.Ö. Özer and M. Wang, Longtime dynamics for a novel piezoelectric beam model with creep and thermoviscoelastic effects. Nonlinear Anal. Real World Appl. 68 (2022) Article number 103666. [Google Scholar]
  32. B. Feng and A.Ö. Özer, Stability results for piezoelectric beams with long-range memory effects in the Boundary. Math. Nachr. 296 (2023) 4206–4235. [Google Scholar]
  33. J. Hao and J. Yang, New general decay results for a fully dynamic piezoelectric beam system with fractional delays under memory boundary controls. Math. Meth. Appl. Sci. 47 (2024) 229–267. [Google Scholar]
  34. J.M. Wang and B.Z. Guo, On dynamic behavior of a hyperbolic system derived from a thermo-elastic equation with memory type. J. Franklin Inst. 344 (2007) 75–96. [Google Scholar]
  35. K.P. Jin, J. Liang and T.J. Xiao, Coupled second order evolution equations with fading memory: Optimal energy decay rate. J. Differ. Equ. 257 (2014) 1501–1528. [Google Scholar]
  36. J.E.M. Rivera and M.G. Naso, Optimal energy decay rate for a class of weakly dissipative second-order systems with memory. Appl. Math. Lett. 23 (2010) 743–746. [Google Scholar]
  37. A.M. Al-Mahdi, M.M. Al-Gharabli, A. Guesmia and S.A. Messaoudi, New decay results for a viscoelastic-type Timoshenko system with infinite Memory. Z. Angew. Math. Phys. 72 (2021) Article number 22. [Google Scholar]
  38. B. Chentouf and A. Guesmia, Well-posedness and stability results for the Korteweg–de Vries–Burgers and Kuramoto–Sivashinsky equations with infinite memory: a history approach. Nonlinear Anal. Real World Appl. 65 (2022) Article number 103508. [Google Scholar]
  39. B. Feng and T.A. Apalara, Optimal decay for a porous elasticity system with memory. J. Math. Anal. Appl. 470 (2018) 1108–1128. [Google Scholar]
  40. Z.Y. Liu, B.P. Rao and Q. Zhang, Polynomial stability of the Rao–Nakra beam with a single internal viscous Damping. J. Differ. Equ. 269 (2020) 6125–6162. [CrossRef] [Google Scholar]
  41. C.M. Dafermos, An abstract Volterra equation with application to linear viscoelasticity. J. Differ. Equ. 7 (1970) 554–569. [Google Scholar]
  42. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer, New York (2011). [Google Scholar]
  43. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences. Springer-Verlag, New York (1983). [Google Scholar]
  44. C.J.K. Batty, R. Chill and Y. Tomilov, Fine scales of decay of operator semigroups. J. Eur. Math. Soc. 18 (2016) 853–929. [Google Scholar]
  45. A. Borichev and Y. Tomilov, Optimal polynomial decay of functions and operator semigroups. Math. Ann. 347 (2010) 455–478. [Google Scholar]
  46. J. Rozendaal, D. Seifert and R. Stahn, Optimal rates of decay for operators semigroups on Hilbert spaces. Adv. Math. 346 (2019) 359–388. [CrossRef] [MathSciNet] [Google Scholar]
  47. Z.Y. Liu and B.P. Rao, Characterization of polynomial decay rate for the solution of linear evolution equation. Z. Angew. Math. Phys. 56 (2005) 630–644. [Google Scholar]
  48. J. Hao, Z. Liu and J. Yong, Regularity analysis for an abstract system of coupled hyperbolic and parabolic equations. J. Differ. Equ. 259 (2015) 4763–4798. [CrossRef] [Google Scholar]
  49. J. Shen, T. Tang and L.L. Wang, Spectral Methods: Algorithms, Analysis and Applications. Springer Science & Business Media, Berlin (2011). [Google Scholar]
  50. C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary. SIAM J. Control Optim. 30 (1992) 1024–1065. [Google Scholar]

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