An Exponential Stability Result of a Timoshenko System with Thermoelasticity with Second Sound and in the Presence of Delay

An Exponential Stability Result of a Timoshenko System with Thermoelasticity with Second Sound... In this paper, we consider a one-dimensional linear thermoelastic system of Timoshenko type with a delay, where the heat flux is given by Cattaneo’s law. We prove an exponential decay result under a smallness condition on the delay and a stability number introduced first in Santos et al. (J Diff Eqs 253:2715–2733, 2012 ), using a method different from that of Santos et al. (J Diff Eqs 253:2715–2733, 2012 ). We also reproduce the polynomial decay of Santos et al. (J Diff Eqs 253:2715–2733, 2012 ) using the multiplier method in the case of absence of delay. The polynomial decay issue in the presence of a small delay is an open question. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

An Exponential Stability Result of a Timoshenko System with Thermoelasticity with Second Sound and in the Presence of Delay

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Publisher
Springer US
Copyright
Copyright © 2015 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-014-9266-0
Publisher site
See Article on Publisher Site

Abstract

In this paper, we consider a one-dimensional linear thermoelastic system of Timoshenko type with a delay, where the heat flux is given by Cattaneo’s law. We prove an exponential decay result under a smallness condition on the delay and a stability number introduced first in Santos et al. (J Diff Eqs 253:2715–2733, 2012 ), using a method different from that of Santos et al. (J Diff Eqs 253:2715–2733, 2012 ). We also reproduce the polynomial decay of Santos et al. (J Diff Eqs 253:2715–2733, 2012 ) using the multiplier method in the case of absence of delay. The polynomial decay issue in the presence of a small delay is an open question.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jun 1, 2015

References

  • Feedback stabilization of a class of evolution equations with delay
    Ait Benhassi, EM; Ammari, K; Boulite, S; Maniar, L
  • On the control of a viscoelastic damped Timoshenko-type system
    Guesmia, A; Messaoudi, SA
  • General energy decay estimates of Timoshenko systems with frictional versus viscoelastic damping
    Guesmia, A; Messaoudi, SA

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