Uniform attractors for a nonautonomous extensible plate equation with a strong damping

Abstract

In this paper, we study the long‐time dynamics of solutions to a nonlinear nonautonomous extensible plate equation with a strong damping. Under some suitable assumptions on the initial data, the nonlinear term and external force, we establish the existence of global solutions that generate a family of processes for the problem and obtain uniform attractors corresponding to strong and weak symbol spaces in a bounded domain normalΩ⊆double-struckRn0.3em(n⩾1). Copyright © 2016 John Wiley & Sons, Ltd.

Uniform attractors for non-autonomous plate equations with <inline-formula><tex-math id="M1">\begin{document}$ p $\end{document}</tex-math></inline-formula>-Laplacian perturbation and critical nonlinearities

“…Remark 9. Assume that (g(t), g t (t)) is translation bounded in L ∞ (R; L 2 )∩L 2 loc (R; L 2 ), using the inequality in Lemma 3.1 and technique in [8], the existence of uniform attractor for problem (1)-(3) can be also obtained.…”

“…In the case of one-dimensional model, Ma and Pelicer [20] proved the uniqueness with weak damping ku t when p ≥ 3. To our best knowledge, the non-autonomous plate equations like (1)- (2) and related models have not been considered early since there is no invariance for the solution operator except the literatures [8], [23].…”

“…We note that conditions (7) and (8) include the critical exponents for the growth of f and p, respectively.…”

Uniform attractors for the non-autonomous suspension bridge equation with time delay

“…Theorem 2.5 ( [30,32]) Let E be a complete metric space, {U σ (t, τ )}, σ ∈ Σ be a family of processes on E satisfying the translation identity (2.8)-(2.9). Then {U σ (t, τ )}, σ ∈ Σ has a compactly uniform attractor (w.r.t.…”

Global Attractors of the Extensible Plate Equations with Nonlinear Damping and Memory

“…Shen and Ma [21] studied the existence of the random attractor for plate equations with memory and additive 2 Journal of Function Spaces white noise. On the other hand, the asymptotic behavior of solutions for the extensible plate equations without memory affection was studied by several authors in [24][25][26][27].…”