Large Diffusivity and Rate of Convergence of Attractors in Parabolic Systems

TL;DR

This paper investigates how quickly attractors in parabolic systems with large diffusion converge, identifying the precise moment of spatial homogenization and providing optimal estimates for attractor continuity.

Contribution

It introduces exact convergence rates and demonstrates optimality of these estimates in the context of large diffusion parabolic systems.

Findings

Spatial homogenization occurs at a specific, identifiable moment.

The paper provides optimal estimates for the continuity of attractors.

Convergence rates are explicitly characterized for systems with large diffusion.

Abstract

In this paper we are concerned with rate of convergence of parabolic systems with large diffusion. We will exhibit the exact moment that spatial homogenization occurs and estimate the continuity of attractors by a rate of convergence. We will show an example where our estimate is optimal.