@article{Wang2025, 
author = {Xuan Wang and Wei Wang},
title = {The time-dependent attractor for beam equation with rotational inertia and structural damping},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {7},
pages = {15206-15230},
keywords = {rotational inertia, regularity, time-dependent global attractors, structural damping},
url = {https://www.sciopen.com/article/10.3934/math.2025682},
doi = {10.3934/math.2025682},
abstract = {In this paper, we discussed the asymptotic behavior of the solutions to the beam equation with rotational inertia and structural damping:     ε  (  t  )  (  1  +  (  −  Δ      )          α        )      ∂    t          2        u  +      Δ    2    u  +  γ  (  −  Δ      )          θ            ∂    t    u  +  f  (  u  )  =  g  (  x  )  ,where    ε  (  t  ) was a decreasing bounded function. We found a more optimized subcritical exponent        p          ∗        =            N      +      2      θ              N      −      4       depending on    θ  . Additionally, we showed that when the growth exponent    p of nonlinear terms    f  (  u  ) was within the range    1  ⩽  p  <      p          ∗        , the well-posedness and regularity were established. Finally, within the theory of process on time-dependent spaces, we investigated the existence of the time-dependent attractor by using the contraction function method and more detailed estimates in the time-dependent space              H              t              α        . The results refined and extended the model and the work in literature [Longtime behavior for an extensible beam equation with rotational inertia and structural nonlinear damping, J. Math. Anal. Appl., 496 (2021), 124785.] from general energy space to time-dependent space in some sense.}
}