Existence of pullback attractors for pullback asymptotically compact processes

Bi-space pullback attractors for closed processes

In the description of the long-time behavior of solutions to nonautonomous differential equations the notion of a pullback attractor plays a similar role as the global attractor in autonomous dynamical systems. We present the theorem on the existence of a pullback attractor if the evolution process is a family of closed operators. The abstract result is formulated in the context of the smoothin...

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...

The Pullback Attractors for the Nonautonomous Camassa-Holm Equations

Existence and Regularity of Pullback Attractors for an Incompressible Non-newtonian Fluid with Delays

This paper studies an incompressible non-Newtonian fluid with delays in two-dimensional bounded domains. We first prove the existence and uniqueness of solutions. Then we establish the existence of pullback attractors {AC H (t)}t∈R (has L-regularity), {AC W (t)}t∈R (has H-regularity), and {AE2 H (t)}t∈R (has L-regularity), {A E2 W (t)}t∈R (has H-regularity) corresponding to two different proces...

Pullback attractors for non-autonomous reaction-diffusion equations in Lp

We study the long time behavior of solutions of the non-autonomous Reaction-Diffusion equation defined on the entire space Rn when external terms are unbounded in a phase space. The existence of a pullback global attractor for the equation is established in L(R) and H(R), respectively. The pullback asymptotic compactness of solutions is proved by using uniform a priori estimates on the tails of...