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Existence and Exponential Stability for a Thermoviscoelastic Equation with Boundary Output Feedback Control

  • Kang, Yong Han (Institute of Liberal Education, Catholic University of Daegu)
  • Received : 2015.10.26
  • Accepted : 2016.05.28
  • Published : 2016.06.23

Abstract

In this paper, we consider a thermoviscoelastic equation which has one end fixed and output feedback control at the other end. We prove the existence of solutions using the Galerkin method and then investigate the exponential stability of solutions by using multiplier technique.

Keywords

References

  1. Bao-Zhu Guo, Wei Guo, Adaptive stabilization for a Kirchhoff-type nonlinear beam under boundary output feedback control, Nonlinear Analysis, 66(2007), 427-441 https://doi.org/10.1016/j.na.2005.11.037
  2. Bao-Zhu Guo, Zhi-Chao Shao, On exponential stability of a semilinear wave equation with variable coefficients under the nonlinear boundary feedback, Nonlinear Analysis, 71(2009), 5961-5978 https://doi.org/10.1016/j.na.2009.05.018
  3. J. E. Lagnese, G. Leugering, Uniform stabilization of a nonlinear beam by nonlinear boundary feedback, Journal of Differential Equations, 91(1991), 355-388 https://doi.org/10.1016/0022-0396(91)90145-Y
  4. J. Y. Park, Y. H. Kang, J. A. Kim, Existence and exponential stability for a Euler-Bernoulli beam equation with memory and boundary output feedback control term, Acta Applicandae Mathematicae, 104(2008), 287-301 https://doi.org/10.1007/s10440-008-9257-8
  5. M. Fekan, Free vibrations of beams on bearings with nonlinear elastic responses, Journal of Differential Equations, 154(1999), 55-72 https://doi.org/10.1006/jdeq.1998.3561
  6. M. Nakao, J. E. M. Rivera, The contact problem in thermoviscoelastic materials, Journal of Mathematical Analysis and Applications, 264(2001), 522-545 https://doi.org/10.1006/jmaa.2001.7686
  7. T. F. Ma, Existence results for a model of nonlinear beam on elastic bearings, Applied Mathematics Letters, 13(2000), 11-15 https://doi.org/10.1016/S0893-9659(00)00026-4