Global Attractors of Non-autonomous Lattice Dynamical Systems

TL;DR

This paper investigates the existence and properties of global attractors in non-autonomous lattice dynamical systems, demonstrating their dissipativity, asymptotic compactness, and establishing conditions for their existence.

Contribution

It provides new results on the existence and characterization of global attractors for non-autonomous lattice systems, including proofs of dissipativity and asymptotic compactness.

Findings

Proved dissipativity of the systems.

Established asymptotic compactness.

Confirmed existence of compact global attractors.

Abstract

The aim of this paper is studying the compact global attractors for non-autonomous lattice dynamical systems of the form $u_{i}'=\nu (u_{i-1}-2u_i+u_{i+1})-\lambda u_{i}+f(u_i)+f_{i}(t)\ (i\in \mathbb Z,\ \lambda >0)$. We prove their dissipativness, asymptotic compactness and then the existence of compact global attractors.