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Stability Results for a Timoshenko System with a Fractional Operator in the Memory

  • María AstudilloEmail author
  • Higidio Portillo Oquendo
Article
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Abstract

We study the asymptotic behavior of Timoshenko systems with a fractional operator in the memory term depending on a parameter \(\theta \in [0,1]\) and acting only on one equation of the system. Considering exponentially decreasing kernels, we find exact decay rates. To be precise, we show that for \(\theta \in [0,1)\), the system decay polynomially with rates that depend on the value of the difference of the wave propagation speeds. We also prove that these decay rates are optimal. Moreover, when \(\theta =1\) and the equations have the same propagation speeds we obtain the exponential decay of the solutions.

Keywords

Timoshenko system Fractional damping Memory term Exponential stability Polynomial decay 

Notes

Acknowledgements

The first author has been partially supported by PNPD/CAPES (CAPES Postdoctoral National Program).

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mathematics Postgraduate ProgramFederal University of ParanáCuritibaBrazil

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