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Applied Mathematics & Optimization

, Volume 73, Issue 1, pp 165–194 | Cite as

On a Class of Nonlinear Viscoelastic Kirchhoff Plates: Well-Posedness and General Decay Rates

  • M. A. Jorge SilvaEmail author
  • J. E. Muñoz Rivera
  • R. Racke
Article

Abstract

This paper is concerned with well-posedness and energy decay rates to a class of nonlinear viscoelastic Kirchhoff plates. The problem corresponds to a class of fourth order viscoelastic equations of \(p\)-Laplacian type which is not locally Lipschitz. The only damping effect is given by the memory component. We show that no additional damping is needed to obtain uniqueness in the presence of rotational forces. Then, we show that the general rates of energy decay are similar to ones given by the memory kernel, but generally not with the same speed, mainly when we consider the nonlinear problem with large initial data.

Keywords

Kirchhoff plates Well-posedness \(p\)-Laplacian General decay rates 

Mathematics Subject Classification

35B35 35B40 35L75 74D99 

Notes

Acknowledgments

The authors have been supported by the Brazilian Agency CNPq within the Project ”Ciências sem Fronteiras”, Grant #402689/2012-7. The first author was also partially supported by the CNPq Grant #441414/2014-1.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • M. A. Jorge Silva
    • 1
    Email author
  • J. E. Muñoz Rivera
    • 2
    • 3
  • R. Racke
    • 4
  1. 1.Department of MathematicsState University of LondrinaLondrinaBrazil
  2. 2.National Laboratory of Scientific ComputationPetrópolisBrazil
  3. 3.Institute of MathematicsFederal University of Rio de JaneiroRio de JaneiroBrazil
  4. 4.Department of Mathematics and StatisticsUniversity of KonstanzKonstanzGermany

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