Attractors and their continuity for an extensible beam equation with rotational inertia and nonlocal energy damping

Well-posedness and strong attractors for a beam model with degenerated nonlocal strong damping

“…The global attractor theory of beam equations with nonlocal damping has received much more attention in recent years (cf. [6,7,15,21,22,23,25,26,31,32] and reference therein). Motivated by model (1.6), the authors in [26] studied a more general case…”

“…Finally, they obtained the strong global and exponential attractors and their robustness on the perturbed parameter κ ∈ Λ, where the "strong" means that the compactness, the attractiveness and the finiteness of the fractal dimension of the attractors are all in the topology of the regular space H 2 . Taking into account the rotational force in beam equations, the authors in [25] considered the following model…”

“…Specifically, for the non-degenerate case, one can obtain the well-posedness of weak solution by approximating regular solutions in a standard way (cf. [25,26]). When considering nonlocal weak damping such as ( ∆u 2 + u t…”