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Journal of Dynamical and Control Systems

, Volume 25, Issue 2, pp 263–273 | Cite as

Asymptotic Stability for the Second Order Evolution Equation with Memory

  • Muhammad I. MustafaEmail author
Article

Abstract

In this paper, we consider an abstract viscoelastic equation. We use memory-type damping with a general assumption on the relaxation function and establish explicit energy decay result from which we can recover the optimal exponential and polynomial rates. Our result generalizes the earlier related results in the literature.

Keywords

General decay Viscoelastic damping Relaxation function 

Mathematics Subject Classification (2010)

35B40 74D99 93D15 93D20 

Notes

Acknowledgments

The author thanks University of Sharjah for its continuous support.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SharjahSharjahUnited Arab Emirates

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