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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 14
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Research Article

Well-posedness and exponential stability of a thermoelastic system with internal delay

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Pages 4851-4865 | Received 21 Jul 2020, Accepted 01 Jan 2021, Published online: 18 Jan 2021

References

  • Racke R. Instability of coupled systems with delay. Commun Pure Appl Anal. 2012;11:1753–1773.
  • Racke R. Thermoelasticity with second sound: exponential stability in linear and nonlinear 1-d. Math Meth Appl Sci. 2002;25:409–441.
  • Hansen SW. Exponential energy decay in a linear thermoelastic rod. J Math Anal Appl. 1992;167:429–442.
  • Rivera M. Energy decay rate in linear thermoelasticity. Funkcial Ekvac. 1992;35:19–30.
  • Liu Z, Zheng S. Semigroups associated with dissipative systems. Research Notes in Mathematics, Vol. 398 .Chapman & Hall/CRC: Boca Raton; 1999.
  • Suh IH, Bien Z. Use of time delay action in the controller design. IEEE Trans Autom Control. 1980;25:600–603.
  • PM Jordan WD, Mickens R. A note on the delayed heat equation: instability with respect to initial data. Mech Res Comm. 2008;35:414–420.
  • Bátkai A, Piazzera S. Semigroups for delay equations. Wellesley, MA: A. K. Peters; 2005. (Research Notes in Mathematics; Vol. 10).
  • Datko R. Two examples of ill-posedness with respect to time delays revised. IEEE Trans Autom Control. 1997;42:511–515.
  • Datko R. Not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks. SIAM J Control Optim. 1988;26:697–713.
  • Datko R, Lagnese J, Polis P. An example of the effect of time delays in boundary feedback stabilization of wave equations. SIAM J Control Optim. 1986;24:152–156.
  • Nicaise S, Pignotti C. Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks. SIAM J Control Optim. 2006;45:1561–1585.
  • Benhassi EMA, Ammari K, Boulite S, et al. Feedback stabilization of a class of evolution equation with delay. J Evol Equ. 2009;9:103–121.
  • Ammari K, Nicaise S. Stabilization of elastic systems by collocated feedback. Cham: Springer; 2015. (Lecture Notes in Mathematics; Vol. 2124).
  • Nicaise S, Pignotti C. Well-posedness and stability results for nonlinear abstract evolution equations with time delays. J Evol Equ. 2018;18:947–971.
  • Messaoudi SA, Fareh A, Doudi N. Well posedness and exponential stability in a wave equation with a strong damping and a strong delay. J Math Phys. 2016;57:111501.
  • Ammari K, Nicaise S, Pignotti C. Stability of abstract-wave equation with delay and a kelvin-voigt damping. Asymptot Anal. 2015;95:21–38.
  • Mustapha MI, Kafini M. Exponential decay in thermoelastic systems with internal distributed delay. Palest J Math. 2013;2:287–299.
  • Engel KJ, Nagel R. One-parameter semigroups for linear evolution equations. New York, Berlin, Heidelberg; 1999. (Graduate Texts in Mathematics; Vol. 194).

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