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

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