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...

The notion of an attractor is one of the basic concepts in the theory of dynamical systems. For deterministic systems this notion has been of importance since several decades. Since about fifteen years also attractors for stochastic systems have been taken under consideration. The crucial obstacle came from the fact that the classical approach, using the Markov property of individual solutions ...

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...

We study Galerkin approximation of pullback attractors for a nonautonomous nonlocal parabolic equation. show that the $ n $th system has attractor in $-dimensional subspace Lebesgue space. then prove sequence is uniformly backward bounded and solutions converges on any set. Using these results, we establish upper semi-convergence towards original infinite-dimensional system.

In this paper we study the asymptotic dynamics for the nonautonomous stochastic strongly damped wave equation driven by additive noise defined on unbounded domains. First we introduce a continuous cocycle for the equation and then investigate the existence and uniqueness of tempered random attractors which pullback attract all tempered random sets.

The theory of global attractors for autonomous systems as developed by Hale in [7] owes much to examples arising in the study of retarded functional differential equations [8] (for slightly different approaches see Babin and Vishik [1], Ladyzhenskaya [13], or Temam [16]). Although the classical theory can be extended in a relatively straightforward manner to deal with time-periodic equations, g...

We show the lower semicontinuity of the family of pullback attractors for the singularly nonautonomous plate equation with structural damping utt + a(t, x)ut + (−∆)ut + (−∆)u+ λu = f(u), in the energy space H2 0 (Ω)×L2(Ω) under small perturbations of the damping term a.