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

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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.

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Acknowledgements

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

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  1. Mathematics Postgraduate Program, Federal University of Paraná, Curitiba, Brazil

    María Astudillo & Higidio Portillo Oquendo

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  1. María Astudillo
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  2. Higidio Portillo Oquendo
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Correspondence to María Astudillo.

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Astudillo, M., Portillo Oquendo, H. Stability Results for a Timoshenko System with a Fractional Operator in the Memory. Appl Math Optim 83, 1247–1275 (2021). https://doi.org/10.1007/s00245-019-09587-w

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