Pullback exponential attractors for nonautonomous equations Part I: Semilinear parabolic problems

Pullback Exponential Attractors for Nonautonomous Reaction-Diffusion Equations

Under the assumption that g t ( ) is translation bounded in loc L R L 4 4 ( ; ( )) Ω , and using the method developed in [3], we prove the existence of pullback exponential attractors in H 1 0 ( ) Ω for nonlinear reaction diffusion equation with polynomial growth nonlinearity( p 2 ≥ is arbitrary).

Regularity and Exponential Growth of Pullback Attractors for Semilinear Parabolic Equations Involving the Grushin Operator

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 ...

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...

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...

The Pullback Attractors for the Nonautonomous Camassa-Holm Equations