English

A Unified Theory for Inertial Manifolds, Saddle Point Property and Exponential Dichotomy

Analysis of PDEs 2021-11-24 v1

Abstract

Inertial manifold theory, saddle point property and exponential dichotomy have been treated as different topics in the literature with different proofs. As a common feature, they all have the purpose of `splitting' the space to understand the dynamics. We present a unified proof for the inertial manifold theorem, which as a local consequence yields the saddle-point property with a fine structure of invariant manifolds and the roughness of exponential dichotomy. In particular, we use these tools in order to establish the hyperbolicity of certain global solutions for non-autonomous parabolic partial differential equations.

Keywords

Cite

@article{arxiv.2111.11469,
  title  = {A Unified Theory for Inertial Manifolds, Saddle Point Property and Exponential Dichotomy},
  author = {Alexandre N. Carvalho and Phillipo Lappicy and Estefani M. Moreira and Alexandre N. Oliveira-Sousa},
  journal= {arXiv preprint arXiv:2111.11469},
  year   = {2021}
}