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

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2016
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Silva, M. A. Jorge
Rivera, J. E. Muñoz
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Applied Mathematics & Optimization. 2016, 73(1), pp. 165-194. ISSN 0095-4616. eISSN 1432-0606. Available under: doi: 10.1007/s00245-015-9298-0
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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.

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ISO 690SILVA, M. A. Jorge, J. E. Muñoz RIVERA, Reinhard RACKE, 2016. On a Class of Nonlinear Viscoelastic Kirchhoff Plates : Well-Posedness and General Decay Rates. In: Applied Mathematics & Optimization. 2016, 73(1), pp. 165-194. ISSN 0095-4616. eISSN 1432-0606. Available under: doi: 10.1007/s00245-015-9298-0
BibTex
@article{Silva2016Class-33954,
  year={2016},
  doi={10.1007/s00245-015-9298-0},
  title={On a Class of Nonlinear Viscoelastic Kirchhoff Plates : Well-Posedness and General Decay Rates},
  number={1},
  volume={73},
  issn={0095-4616},
  journal={Applied Mathematics & Optimization},
  pages={165--194},
  author={Silva, M. A. Jorge and Rivera, J. E. Muñoz and Racke, Reinhard}
}
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