Uniform nonautonomous attractors under discretization

Uniform Nonautonomous Attractors under Discretization

A nonautonomous or cocycle dynamical system that is driven by an autonomous dynamical system acting on a compact metric space is assumed to have a uniform pullback attractor. It is shown that discretization by a one-step numerical scheme gives rise to a discrete time cocycle dynamical system with a uniform pullback attractor, the component subsets of which converge upper semi continuously to th...

Finite Dimensional Uniform Attractors for the Nonautonomous Camassa-Holm Equations

and Applied Analysis 3 and in H1 Ω , respectively, observe that H⊥, the orthogonal complement of H in L2 Ω , is {∇p : p ∈ H1 Ω } cf. 11 or 12 . ii We denote P : L2 Ω 3 → H the L2 orthogonal projection, usually referred as Helmholtz-Leray projector, and by A −PΔ the Stokes operator with domain D A H2 Ω 3 ∩ V . Notice that in the case of periodic boundary condition, A −Δ|D A is a selfadjoint posi...

The Finite-Dimensional Uniform Attractors for the Nonautonomous g-Navier-Stokes Equations

Pullback attractors of nonautonomous reaction–diffusion equations

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...

Nonautonomous Discrete Dynamics: Discretization and Taylor Approximation

In this talk, we consider a class of nonautonomous difference equations (recursions) possessing an attractive invariant manifold in the extended state space. It is our aim to study the behavior of this manifold, as well as of its corresponding asymptotic phase under perturbation. Our framework is sufficiently general to include discrete counterparts of (center-)unstable and inertial manifolds. ...