On Fractal Dimension of Global and Exponential Attractors for Dissipative Higher Order Parabolic Problems in $$\mathbb {R}^N$$ with General Potential

Pullback attractors via quasi-stability for non-autonomous lattice dynamical systems

“…In our setting specific properties of the right-hand side of the system in (1) interplay with the properties of the bounded linear operator on the left-hand side to guarantee the existence of pullback global and exponential attractors for a suitable universe of attracted families of bounded subsets of the space 2 of square summable double-sided real sequences. This cooperation was first observed for lattice dynamical systems in [10] in the autonomous case (see also [11]). Here we follow these ideas in the context of time dependent nonlinearities by developing a concept of quasi-stability of an evolution process.…”

“…Proof. By (11) for any D = {D(t) : t ∈ R} ∈ D u there exists R D > 0 such that u 0 R D for any u 0 ∈ D(s) with s 0. Let r D,0 0 be such that e −2γ0r R 2 D 1 for r r D,0 .…”