Gromov-Hausdorff stability of inertial manifolds under perturbations of the domain and equation

TL;DR

This paper investigates how inertial manifolds in reaction-diffusion equations change continuously when the domain or the equations themselves are slightly perturbed, using Gromov-Hausdorff distances to measure stability.

Contribution

It introduces a framework for analyzing the stability of inertial manifolds under domain and equation perturbations using Gromov-Hausdorff metrics.

Findings

Inertial manifolds exhibit Gromov-Hausdorff stability under perturbations.

Continuous dependence of inertial manifolds on domain and equation changes.

Stability results for dynamical systems induced by reaction-diffusion equations.

Abstract

In this paper, we study the Gromov-Hausdorff stability and continuous dependence of the inertial manifolds under perturbations of the domain and equation. More precisely, we use the Gromov-Hausdorff distances between two inertial manifolds and two dynamical systems to consider the continuous dependence of the inertial manifolds and the stability of the dynamical systems on inertial manifolds induced by the reaction diffusion equations under perturbations of the domain and equation.