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arXiv · 2210.16851

Dynamics of a class of extensible beams with degenerate and non-degenerate nonlocal damping

Eduardo H. Gomes Tavares·Marcio A. Jorge Silva·Vando Narciso·André Vicente
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Abstract

This work is concerned with new results on long-time dynamics of a class of hyperbolic evolution equations related to extensible beams with three distinguished nonlocal nonlinear damping terms. In the first possibly degenerate case, the results feature the existence of a family of compact global attractors and a thickness estimate for their Kolmogorov's $\varepsilon$-entropy. Then, in the non-degenerate context, the structure of the helpful nonlocal damping leads to the existence of finite-dimensional compact global and exponential attractors. Lastly, in a degenerate and critical framework, it is proved the existence of a bounded closed global attractor but not compact. To the proofs, we provide several new technical results by means of refined estimates that open up perspectives for a new branch of nonlinearly damped problems.

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Eduardo H. Gomes Tavares, Marcio A. Jorge Silva, Vando Narciso, André Vicente. 2022-10-30. Dynamics of a class of extensible beams with degenerate and non-degenerate nonlocal damping. https://arxiv.org/abs/2210.16851

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