We consider the pullback attractors for non-autonomous dynamical systems generated by stochastic lattice differential equations with non-autonomous deterministic terms. We first establish a sufficient condition for existence of pullback attractors of lattice dynamical systems with both non-autonomous deterministic and random forcing terms. As an application of the abstract theory, we prove the ...

2 Perturbed dynamics of parametrized systems 7 2.1 The inflation of cocycle dynamics . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Inflation through differential inclusions . . . . . . . . . . . . . . . . . 7 2.1.2 Inflation through additive controls . . . . . . . . . . . . . . . . . . . . 8 2.1.3 Inflation through chain–connectedness . . . . . . . . . . . . . . . . . 8 2.2 Inflated p...

We will study the upper semicontinuity of pullback attractors for the 3D nonautonomouss Benjamin-Bona-Mahony equations with external force perturbation terms. Under some regular assumptions, we can prove the pullback attractors A(ε)(t) of equation, u(t)-Δu(t)-νΔu+∇·(-->)F(u)=εg(x,t), x ∈ Ω, converge to the global attractor A of the above-mentioned equation with ε = 0 for any t ∈ R.

In this paper, firstly we introduce the concept of norm-to-weak continuous cocycle in Banach space and give a technical method to verify this kind of continuity, then we obtain some abstract results for the existence of pullback attractors about this kind of cocycle, using the measure of noncompactness. As an application, we prove the existence of pullback attractors in H 1 0 of the cocycle ass...

The authors consider non-autonomous dynamical behavior of wave-type evolutionary equations with nonlinear damping and critical nonlinearity. These type of wave equations are formulated as continuous non-autonomous dynamical systems (cocycles). A sufficient and necessary condition for the existence of pullback attractors is established. The required compactness for the existence of pullback attr...

and Applied Analysis 3 The content of the paper is as follows. In Section 2, for the convenience of the reader, we recall some concepts and results on function spaces and pullback attractors which we will use. In Section 3, we prove the existence of pullback attractors in the spaces S0 Ω and L2p−2 Ω by using the asymptotic a priori estimate method. In Section 4, under additional assumptions of ...

In this work we obtain theoretical results on continuity of selected pullback attractors for a generalized process and consider the when system is asymptotically autonomous. As an example, apply theory nonautonomous problem with reaction diffusion equations dynamical boundary conditions, after that, some additional hypotheses family problems converging to autonomous limit show convergence their...

In this paper, the existence and uniqueness of pullback attractors for the modified Swift-Hohenberg equation defined on R driven by both deterministic non-autonomous forcing and additive white noise are established. We first define a continuous cocycle for the equation in L(R), and we prove the existence of pullback absorbing sets and the pullback asymptotic compactness of solutions when the eq...

*Correspondence: [email protected] 2Department of Applied Mathematics, Donghua University, Shanghai, 201620, P.R. China Full list of author information is available at the end of the article Abstract Our aim in this paper is to study the existence of pullback attractors for the 3D Navier-Stokes-Voigt equations with delays. The forcing term g(t,u(t – ρ(t))) containing the delay is sub-linea...