Estimates on the distance of inertial manifolds

TL;DR

This paper provides estimates on the distance between inertial manifolds for parabolic dynamical systems, relating it to differences in resolvent operators and nonlinearities across different phase spaces.

Contribution

It introduces a method to estimate inertial manifold distances considering differences in phase spaces, resolvent operators, and nonlinearities.

Findings

Derived explicit bounds for inertial manifold distances

Linked manifold distances to resolvent and nonlinearity differences

Applicable to systems in different phase spaces

Abstract

In this paper we obtain estimates on the distance of inertial manifolds for dynamical systems generated by evolutionary parabolic type equations. We consider the situation where the systems are defined in different phase spaces and we estimate the distance in terms of the distance of the resolvent operators of the corresponding elliptic operators and the distance of the nonlinearities of the equations.