Scaling and Saturation in Infinite-Dimensional Control Problems with Applications to Stochastic Partial Differential Equations
Probability
2018-09-21 v2 Analysis of PDEs
Dynamical Systems
Abstract
We establish the dual notions of scaling and saturation from geometric control theory in an infinite-dimensional setting. This generalization is applied to the low-mode control problem in a number of concrete nonlinear partial differential equations. We also develop applications concerning associated classes of stochastic partial differential equations (SPDEs). In particular, we study the support properties of probability laws corresponding to these SPDEs as well as provide applications concerning the ergodic and mixing properties of invariant measures for these stochastic systems.
Cite
@article{arxiv.1706.01997,
title = {Scaling and Saturation in Infinite-Dimensional Control Problems with Applications to Stochastic Partial Differential Equations},
author = {Nathan E. Glatt-Holtz and David P. Herzog and Jonathan C. Mattingly},
journal= {arXiv preprint arXiv:1706.01997},
year = {2018}
}