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Exponential Characterization in Linear Viscoelasticity Under Delay Perturbations

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Abstract

We present a complete characterization of the (uniform) exponential stabilization for a class of viscoelastic models under small delay perturbations. The main ingredient under consideration is the notion of admissible kernels. While in the standard literature it is mostly common to request a exponential/general kernel as a sufficient condition for the exponential/general stability of the whole viscoelastic system under study, here our objective is to employ the much more general concept of admissible kernels and prove that it is not only sufficient but also a necessary assumption for exponential stability in linear viscoelasticity under small delay perturbations.

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Acknowledgements

The authors thank the referees for their valuable remarks on an earlier version of this work, which led the authors to reach this refined final version.

Funding

Marcio A. Jorge Silva has been supported by the CNPq, grant 301116/2019-9. To F. Ma has been supported by the CNPq, grant 315165/2021-9.

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Authors and Affiliations

  1. Department of Mathematics, State University of Londrina, Londrina, PR, 86057-970, Brazil

    E. H. Gomes Tavares & M. A. Jorge Silva

  2. Department of Mathematics, University of Brasília, Brasília, DF, 70910-900, Brazil

    T. F. Ma

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  1. E. H. Gomes Tavares
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  2. M. A. Jorge Silva
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  3. T. F. Ma
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Correspondence to E. H. Gomes Tavares.

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M. A. J. Silva: Supported by the CNPq, grant 301116/2019-9.

T. F. Ma: Supported by the CNPq, grant 315165/2021-9.

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Tavares, E.H.G., Silva, M.A.J. & Ma, T.F. Exponential Characterization in Linear Viscoelasticity Under Delay Perturbations. Appl Math Optim 87, 27 (2023). https://doi.org/10.1007/s00245-022-09934-4

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