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Exact decay rates for coupled plates with partial fractional dam**

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Abstract

In this work, we study the asymptotic behavior of a system of two-coupled plate equations where one of these equations is conservative and the other one has dissipative properties. The dissipative mechanism is given by the fractional dam** \((-\Delta )^{\theta }v_t\) where \(\theta \) lies in the interval [0, 1]. We show that the semigroup decays polynomially with a rate that depends on \(\theta \) and some relations between the structural coefficients of the system. Explicit decay rates are obtained.

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Acknowledgements

The authors are grateful to the referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Federal University of Paraná, Curitiba, Brazil

    Higidio Portillo Oquendo

  2. Department of Mathematics, Federal University of Technology of Paraná, Pato Branco, Brazil

    Fredy Maglorio Sobrado Suárez

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  1. Higidio Portillo Oquendo
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  2. Fredy Maglorio Sobrado Suárez
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Correspondence to Higidio Portillo Oquendo.

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Portillo Oquendo, H., Sobrado Suárez, F.M. Exact decay rates for coupled plates with partial fractional dam**. Z. Angew. Math. Phys. 70, 88 (2019). https://doi.org/10.1007/s00033-019-1135-x

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  • DOI: https://doi.org/10.1007/s00033-019-1135-x

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