Approximation of Attractors of Nonautonomous Lattice Dynamical Systems

David Cheban; Andrei Sultan

paper

Approximation of Attractors of Nonautonomous Lattice Dynamical Systems

arXiv:2605.18465

Abstract

The aim of this paper is to study the finite-dimensional approximations of the nonautonomous lattice dynamical systems of the form $u_{i}^{'} = ν (u_{i - 1} - 2 u_{i} + u_{i + 1}) - λ u_{i} + F (u_{i}) + f_{i} (t) (i \in Z) (*)$ . We show that the finite-dimensional approximations for (*) are uniformly dissipative. The upper semi-continuous convergence of the attractors of the finite-dimensional approximations is established.