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

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* Dedicated to the memory of Professor Igor Chueshov

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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  • 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.

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


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