Pullback attractors for generalized Korteweg–de Vries–Burgers 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...

The Pullback Attractors for the Nonautonomous Camassa-Holm Equations

Upper Semicontinuity of Pullback Attractors for Non-autonomous Generalized 2d Parabolic Equations

This paper is concerned with a generalized 2D parabolic equation with a nonautonomous perturbation −∆ut + α ∆ut + μ∆ u+∇ · −→ F (u) +B(u, u) = ǫg(x, t). Under some proper assumptions on the external force term g, the upper semicontinuity of pullback attractors is proved. More precisely, it is shown that the pullback attractor {Aǫ(t)}t∈R of the equation with ǫ > 0 converges to the global attract...

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...

Pullback Attractors for Non-autonomous Parabolic Equations Involving Grushin Operators

Using the asymptotic a priori estimate method, we prove the existence of pullback attractors for a non-autonomous semilinear degenerate parabolic equation involving the Grushin operator in a bounded domain. We assume a polynomial type growth on the nonlinearity, and an exponential growth on the external force. The obtained results extend some existing results for non-autonomous reaction-diffusi...