The inflation of nonautonomous systems and their pullback attractors ∗ †
نویسندگان
چکیده
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 pullback attractors . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Existence of inflated pullback attractors . . . . . . . . . . . . . . . . . . . . 10
منابع مشابه
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.
متن کاملLyapunov’s Second Method for Nonautonomous Differential Equations
Converse Lyapunov theorems are presented for nonautonomous systems modelled as skew product flows. These characterize various types of stability of invariant sets and pullback, forward and uniform attractors in such nonautonomous systems. MSC subject classification: 37B25, 37B55, 93D30
متن کاملPullback 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...
متن کاملPullback D-attractors for non-autonomous partly dissipative reaction-diffusion equations in unbounded domains
At present paper, we establish the existence of pullback $mathcal{D}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $L^2(mathbb{R}^n)times L^2(mathbb{R}^n)$. In order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{D}$-absorbing set, is pullback $widehat{D}_0$-asymptotically compact.
متن کاملUpper Semicontinuity of Pullback Attractors for the 3D Nonautonomous Benjamin-Bona-Mahony Equations
We will study the upper semicontinuity of pullback attractors for the 3D nonautonomouss Benjamin-Bona-Mahony equations with external force perturbation terms. Under some regular assumptions, we can prove the pullback attractors A(ε)(t) of equation, u(t)-Δu(t)-νΔu+∇·(-->)F(u)=εg(x,t), x ∈ Ω, converge to the global attractor A of the above-mentioned equation with ε = 0 for any t ∈ R.
متن کامل