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Solvability of a Dynamic Rational Contact with Limited Interpenetration for Viscoelastic Plates

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Abstract

Solvability of the rational contact with limited interpenetration of different kind of viscolastic plates is proved. The biharmonic plates, von Kármán plates, Reissner-Mindlin plates, and full von Kármán systems are treated. The viscoelasticity can have the classical (“short memory”) form or the form of a certain singular memory. For all models some convergence of the solutions to the solutions of the Signorini contact is proved provided the thickness of the interpenetration tends to zero.

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Author information

Correspondence to Jiří Jarušek.

Additional information

This work was supported by the institutional research plan RVO 67985840.

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Jarušek, J. Solvability of a Dynamic Rational Contact with Limited Interpenetration for Viscoelastic Plates. Appl Math 65, 43–65 (2020). https://doi.org/10.21136/AM.2020.0216-19

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Keywords

  • dynamic contact problem
  • limited interpenetration
  • viscoelastic plate
  • existence of solution

MSC 2010

  • 35Q74
  • 74D10
  • 74H20
  • 74K20
  • 74M15