Characterization of Cocycle Attractors for Nonautonomous Reaction–Diffusion Equations

Lyapunov Functions for Cocycle Attractors in Nonautonomous Diierence Equations

The construction of a Lyapunov function characterizing the pullback attraction of a cocycle attractor of a nonautonomous discrete time dynamical system involving Lipschitz continuous mappings is presented.

Attractors for Nonautonomous Parabolic Equations without Uniqueness

Using the theory of uniform global attractors of multivalued semiprocesses, we prove the existence of a uniform global attractor for a nonautonomous semilinear degenerate parabolic equation in which the conditions imposed on the nonlinearity provide the global existence of a weak solution, but not uniqueness. The Kneser property of solutions is also studied, and as a result we obtain the connec...

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...

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 Pullback Attractors for the Nonautonomous Camassa-Holm Equations