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

2022/10/30 by Tavares, Eduardo H. Gomes, Silva, Marcio A. Jorge, Narciso, Vando +1
#35B40 #35B41 #35L75 #37L25 #37L30 #Analysis of PDEs (math.AP) #FOS: Mathematics #G.0

paper · doi:10.48550/arxiv.2210.16851

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 ε-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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