Analysis & PDE

  • Anal. PDE
  • Volume 11, Number 2 (2018), 351-382.

Asymptotic limits and stabilization for the 2D nonlinear Mindlin–Timoshenko system

Fágner Dias Araruna, Pablo Braz e Silva, and Pammella Queiroz-Souza

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Abstract

We show how the so-called von Kármán model can be obtained as a singular limit of a Mindlin–Timoshenko system when the modulus of elasticity in shear k tends to infinity. This result gives a positive answer to a conjecture by Lagnese and Lions in 1988. Introducing damping mechanisms, we also show that the energy of solutions for this modified Mindlin–Timoshenko system decays exponentially, uniformly with respect to the parameter k. As k, we obtain the damped von Kármán model with associated energy exponentially decaying to zero as well.

Article information

Source
Anal. PDE, Volume 11, Number 2 (2018), 351-382.

Dates
Received: 21 July 2016
Revised: 5 May 2017
Accepted: 5 September 2017
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.apde/1513774508

Digital Object Identifier
doi:10.2140/apde.2018.11.351

Mathematical Reviews number (MathSciNet)
MR3724491

Zentralblatt MATH identifier
1375.35534

Subjects
Primary: 35Q74: PDEs in connection with mechanics of deformable solids 74K20: Plates 35B40: Asymptotic behavior of solutions

Keywords
vibrating plates Mindlin–Timoshenko system von Kármán system singular limit uniform stabilization

Citation

Araruna, Fágner Dias; Braz e Silva, Pablo; Queiroz-Souza, Pammella. Asymptotic limits and stabilization for the 2D nonlinear Mindlin–Timoshenko system. Anal. PDE 11 (2018), no. 2, 351--382. doi:10.2140/apde.2018.11.351. https://projecteuclid.org/euclid.apde/1513774508


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