Pullback Attractors for Nonautonomous Degenerate Kirchhoff Equations with Strong Damping

In this paper, we obtain the existence of pullback attractors for nonautonomous Kirchhoff equations with strong damping, which covers the case of possible generation of the stiffness coefficient. For this purpose, a necessary method via “the measure of noncompactness” is established.

Existence and regularity of time-dependent pullback attractors for the non-autonomous nonclassical diffusion equations

In this paper, we prove the existence and regularity of pullback attractors for non-autonomous nonclassical diffusion equations with nonlocal diffusion when the nonlinear term satisfies critical exponential growth and the external force term $h \in L_{l o c}^{2}(\mathbb {R} ; H^{-1}(\Omega )).$ Under some appropriate assumptions, we establish the existence and uniqueness of the weak solution in the time-dependent space $\mathcal {H}_{t}(\Omega )$ and the existence and regularity of the pullback attractors.

Asymptotic Dynamics of Young Differential Equations

We provide a unified analytic approach to study the asymptotic dynamics of Young differential equations, using the framework of random dynamical systems and random attractors. Our method helps to generalize recent results (Duc et al. in J Differ Equ 264:1119–1145, 2018, SIAM J Control Optim 57(4):3046–3071, 2019; Garrido-Atienza et al. in Int J Bifurc Chaos 20(9):2761–2782, 2010) on the existence of the global pullback attractors for the generated random dynamical systems. We also prove sufficient conditions for the attractor to be a singleton, thus the pathwise convergence is in both pullback and forward senses.

Wong–Zakai approximations of second-order stochastic lattice systems driven by additive white noise

In this paper, we study the Wong–Zakai approximations of a class of second-order stochastic lattice systems with additive noise. We first prove the existence of tempered pullback attractors for lattice systems driven by an approximation of the white noise. Then, we establish the upper semicontinuity of random attractors for the approximate system as the size of approximation approaches zero.

Upper semicontinuity of pullback attractors for a nonautonomous damped wave equation

In this paper, we study the local uniformly upper semicontinuity of pullback attractors for a strongly damped wave equation. In particular, under some proper assumptions, we prove that the pullback attractor $\{A_{\varepsilon }(t)\}_{t\in \mathbb{R}}$ { A ε ( t ) } t ∈ R of Eq. (1.1) with $\varepsilon \in [0,1]$ ε ∈ [ 0 , 1 ] satisfies $\lim_{\varepsilon \to \varepsilon _{0}}\sup_{t\in [a,b]} \operatorname{dist}_{H_{0}^{1}\times L^{2}}(A_{\varepsilon }(t),A_{ \varepsilon _{0}}(t))=0$ lim ε → ε 0 sup t ∈ [ a , b ] dist H 0 1 × L 2 ( A ε ( t ) , A ε 0 ( t ) ) = 0 for any $[a,b]\subset \mathbb{R}$ [ a , b ] ⊂ R and $\varepsilon _{0}\in [0,1]$ ε 0 ∈ [ 0 , 1 ] .