Inertial manifolds via spatial averaging: a control-theoretic perspective
Dynamical Systems
2025-03-17 v1 Analysis of PDEs
Abstract
We develop a functional-analytical machinery for studying the quadratic regulator problem arising from spectra perturbations of infinite-dimensional dynamical systems. In particular, we are interested in applications to inertial manifolds theory. For certain nonautonomous Hamiltonian systems associated with such problems, we show the existence and uniform nonoscillation of stable Lagrangian bundles. This is done within the context of the classical frequency condition for stationary problems, as well as for nonstationary problems arising under the conditions of the Spatial Averaging Principle of J. Mallet-Paret and G.R. Sell.
Cite
@article{arxiv.2503.11161,
title = {Inertial manifolds via spatial averaging: a control-theoretic perspective},
author = {Mikhail Anikushin},
journal= {arXiv preprint arXiv:2503.11161},
year = {2025}
}