The time-dependent attractor for beam equation with rotational inertia and structural damping
Year: 2025
Type: article
Abstract: In this paper, we discussed the asymptotic behavior of the solutions to the beam equation with rotational inertia and structural damping:$ \varepsilon(t)(1+(-\Delta) ^{\alpha})\partial^{2}_tu+\Delta^2 u+\gamma(-\Delta)^{\theta}\partial_tu+f(u) = g(x), $where $ \varepsilon(t) $ was a decreasing bounded function. We found a more optimized subcritical exponent $ p^{*} = \frac{N+2\theta}{N-4} $ depending on $ \theta. $ Additionally, we showed that when the growth exponent $ p $ of nonlinear terms $ f(u) $ was within the range $ 1\leqslant 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 $ \mathcal{H}_{t}^{\alpha}. $ 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.
Source: AIMS Mathematics
DOI: 10.3934/math.2025682
Authors: Xuan Wang, Wei Wang
Institution: Northwest Normal University
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,200
OpenAlex ID: W4411856558