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2018 Asymptotic limits and stabilization for the 2D nonlinear Mindlin–Timoshenko system
Fágner Dias Araruna, Pablo Braz e Silva, Pammella Queiroz-Souza
Anal. PDE 11(2): 351-382 (2018). DOI: 10.2140/apde.2018.11.351

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.

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Fágner Dias Araruna. Pablo Braz e Silva. Pammella Queiroz-Souza. "Asymptotic limits and stabilization for the 2D nonlinear Mindlin–Timoshenko system." Anal. PDE 11 (2) 351 - 382, 2018. https://doi.org/10.2140/apde.2018.11.351

Information

Received: 21 July 2016; Revised: 5 May 2017; Accepted: 5 September 2017; Published: 2018
First available in Project Euclid: 20 December 2017

zbMATH: 1375.35534
MathSciNet: MR3724491
Digital Object Identifier: 10.2140/apde.2018.11.351

Subjects:
Primary: 35B40 , 35Q74 , 74K20

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

Rights: Copyright © 2018 Mathematical Sciences Publishers

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