Explicit Construction of a Robust Family of Compact Inertial Manifolds

TL;DR

This paper presents a method to explicitly construct a robust family of compact inertial manifolds, enhancing the understanding of attracting sets in dissipative infinite-dimensional systems, with applications to reaction-diffusion equations.

Contribution

It provides an explicit construction approach for robust compact inertial manifolds, advancing the analysis of attracting sets in dissipative systems.

Findings

Constructed a robust family of compact inertial manifolds.

Applied the method to a reaction-diffusion equation.

Enhanced understanding of attracting sets in infinite-dimensional systems.

Abstract

A construction of a robust family of compact inertial manifolds is presented. The result aims to complete an analysis of certain types of attracting sets for a class of dissipative infinite dimensional dynamical systems. Application to a hyperbolically relaxed Chaffee-Infante reaction diffusion equation is also discussed.