Robustness of exponential attractors for infinite dimensional dynamical systems with small delay and application to 2D nonlocal diffusion delay lattice systems

Abstract

We first present some sufficient conditions for the construction of a robust family of exponential attractors for infinite dimensional dynamical systems with small time delay perturbation. In particular, we prove that this family of exponential attractors is stable in the sense of the symmetric Hausdorff distance as the delay effects vanish. The abstract result is then applied to two-dimensional nonlocal diffusion lattice systems with small delay.