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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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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