Inertial manifolds and finite-dimensional reduction for dissipative PDEs
Analysis of PDEs
2013-03-20 v1
Abstract
These notes are devoted to the problem of finite-dimensional reduction for parabolic PDEs. We give a detailed exposition of the classical theory of inertial manifolds as well as various attempts to generalize it based on the so-called Man\'e projection theorems. The recent counterexamples which show that the underlying dynamics may be in a sense infinite-dimensional if the spectral gap condition is violated as well as the discussion on the most important open problems are also included.
Keywords
Cite
@article{arxiv.1303.4457,
title = {Inertial manifolds and finite-dimensional reduction for dissipative PDEs},
author = {Sergey Zelik},
journal= {arXiv preprint arXiv:1303.4457},
year = {2013}
}
Comments
This manuscript is an extended version of the lecture notes taught by the author as a part of the crash course in the Analysis of Nonlinear PDEs at Maxwell Center for Analysis and Nonlinear PDEs (Edinburgh, November, 8-9, 2012)