Exponential mixing for random nonlinear wave equations: weak dissipation and localized control
Analysis of PDEs
2024-07-23 v1 Dynamical Systems
Optimization and Control
Probability
Abstract
We establish a new criterion for exponential mixing of random dynamical systems. Our criterion is applicable to a wide range of systems, including in particular dispersive equations. Its verification is in nature related to several topics, i.e., asymptotic compactness in dynamical systems, global stability of evolution equations, and localized control problems. As an initial application, we exploit the exponential mixing of random nonlinear wave equations with degenerate damping, critical nonlinearity, and physically localized noise. The essential challenge lies in the fact that the weak dissipation and randomness interact in the evolution.
Cite
@article{arxiv.2407.15058,
title = {Exponential mixing for random nonlinear wave equations: weak dissipation and localized control},
author = {Ziyu Liu and Dongyi Wei and Shengquan Xiang and Zhifei Zhang and Jia-Cheng Zhao},
journal= {arXiv preprint arXiv:2407.15058},
year = {2024}
}