Strong Pullback Attractors of the Nonautonomous Suspension Bridge Equation with Variable Delay

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

The inflation of nonautonomous systems and their pullback attractors ∗ †

2 Perturbed dynamics of parametrized systems 7 2.1 The inflation of cocycle dynamics . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Inflation through differential inclusions . . . . . . . . . . . . . . . . . 7 2.1.2 Inflation through additive controls . . . . . . . . . . . . . . . . . . . . 8 2.1.3 Inflation through chain–connectedness . . . . . . . . . . . . . . . . . 8 2.2 Inflated p...

Pullback Attractors for Nonautonomous 2D-Navier-Stokes Models with Variable Delays

and Applied Analysis 3 Theorem 4 (see [21, 22]). Let X,Y be two Banach spaces satisfy the previous assumptions, and let {U(t, τ)} be amultivalued process onX andY, respectively. Assume that {U(t, τ)} is upper semicontinuous or weak upper semicontinuous on Y. If for fixed t ⩾ τ, τ ∈ R, U(t, τ) maps compact subsets of X into bounded subsets ofP(X), then U(t, τ) is norm-to-weak upper semicontinuou...

Lower Semicontinuity of Pullback Attractors for a Singularly Nonautonomous Plate Equation

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.