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Exponential Stability of a Certain Semigroup and Applications

Abstract

The uniform exponential stability of a C0-semigroup with generator of a special form is proved. Such semigroups arise in the study of various problems of the theory of viscoelasticity. The proved statement is applied to the study of the asymptotic behavior of solutions in the problem of small motions of a viscoelastic body subject to driving forces of a special form.

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Correspondence to D. A. Zakora.

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Original Russian Text © D. A. Zakora, 2018, published in Matematicheskie Zametki, 2018, Vol. 103, No. 5, pp. 702–719.

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Zakora, D.A. Exponential Stability of a Certain Semigroup and Applications. Math Notes 103, 745–760 (2018). https://doi.org/10.1134/S0001434618050073

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  • DOI: https://doi.org/10.1134/S0001434618050073

Keywords

  • C0-semigroup
  • integro-differential equation
  • exponential stability
  • materials with memory
  • asymptotics