July/August 2023 Dynamics of a class of extensible beams with degenerate and non-degenerate nonlocal damping
E.H. Gomes Tavares, M.A. Jorge Silva, V. Narciso, A. Vicente
Adv. Differential Equations 28(7/8): 685-752 (July/August 2023). DOI: 10.57262/ade028-0708-685

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.

Citation

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E.H. Gomes Tavares. M.A. Jorge Silva. V. Narciso. A. Vicente. "Dynamics of a class of extensible beams with degenerate and non-degenerate nonlocal damping." Adv. Differential Equations 28 (7/8) 685 - 752, July/August 2023. https://doi.org/10.57262/ade028-0708-685

Information

Published: July/August 2023
First available in Project Euclid: 10 April 2023

Digital Object Identifier: 10.57262/ade028-0708-685

Subjects:
Primary: 35B40 , 35B41 , 35L75 , 37L25 , 37L30

Rights: Copyright © 2023 Khayyam Publishing, Inc.

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Vol.28 • No. 7/8 • July/August 2023
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