Long-time dynamics for a class of extensible beams with nonlocal nonlinear damping*

Marcio Antonio Jorge da Silva; Vando Narciso

doi:10.3934/eect.2017023

Article Contents

2017, Volume 6, Issue 3: 437-470. Doi: 10.3934/eect.2017023

This issue Previous Article Sensitivity analysis in set-valued optimization under strictly minimal efficiency Next Article Approximate controllability of Sobolev type fractional evolution systems with nonlocal conditions

Long-time dynamics for a class of extensible beams with nonlocal nonlinear damping^*

Marcio Antonio Jorge da Silva^1, , and
Vando Narciso^2,

1.
Department of Mathematics, State University of Londrina, Londrina, 86057-970, Brazil
2.
Center of Exact Sciences, State University of Mato Grosso do Sul, Dourados, 79804-970, Brazil

^† Corresponding author
^† Corresponding author

* Dedicated to the memory of Professor Igor Chueshov

Received: December 31, 2016

Revised: April 30, 2017

Published: October 2017

The first author was supported by supported by CNPq grant 441414/2014-1.
The second author was partially supported by CAPES grant 20132268.

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Abstract

In this paper we consider new results on well-posedness and long-time dynamics for a class of extensible beam/plate models whose dissipative effect is given by the product of two nonlinear terms. The addressed model contains a nonlocal nonlinear damping term which generalizes some classes of dissipations usually given in the literature, namely, the linear, the nonlinear and the nonlocal frictional ones. A first mathematical analysis of such damping term is presented and represents the main novelty in our approach.

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Mathematics Subject Classification: Primary: 35B40, 35B41, 37L30; Secondary: 35L75, 74H40.

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