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Stability of weakly dissipative Reissner–Mindlin–Timoshenko plates: A sharp result

Published online by Cambridge University Press:  27 April 2017

A. D. S. CAMPELO ,
D. S. ALMEIDA JÚNIOR  and
M. L. SANTOS
A. D. S. CAMPELO
Affiliation:
Department of Mathematics – Federal University of Pará, Augusto Corrêa Street, 01, 66075-110, Belém, Pará, Brazil emails: campelo.ufpa@gmail.com, dilberto@ufpa.br, ls@ufpa.br
D. S. ALMEIDA JÚNIOR
Affiliation:
Department of Mathematics – Federal University of Pará, Augusto Corrêa Street, 01, 66075-110, Belém, Pará, Brazil emails: campelo.ufpa@gmail.com, dilberto@ufpa.br, ls@ufpa.br
M. L. SANTOS
Affiliation:
Department of Mathematics – Federal University of Pará, Augusto Corrêa Street, 01, 66075-110, Belém, Pará, Brazil emails: campelo.ufpa@gmail.com, dilberto@ufpa.br, ls@ufpa.br
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Abstract

In the present article, we show that there exists a critical number that stabilizes the Reissner–Mindlin–Timoshenko system with frictional dissipation acting on rotation angles. We identify two speed characteristics v 1 2:=K/ρ1 and v 2 2:=D/ρ2, and we show that the system is exponentially stable if and only if

\begin{equation*}v_{1}^{2}=v_{2}^{2}.\end{equation*}
For v 1 2 ≠ v 2 2, we prove that the system is polynomially stable and determine an optimal estimate for the decay. To confirm our analytical results, we compute the numerical solutions by means of several numerical experiments by using a finite difference method.

Keywords

Reissner-Mindlin-Timoshenko systemwave propagation speedexponential stabilityoptimal decayfinite difference

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Type
Papers
Information
European Journal of Applied Mathematics , Volume 29 , Issue 2 , April 2018 , pp. 226 - 252
Copyright
Copyright © Cambridge University Press 2017 

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