7 papers
Exponential mixing for Korteweg-de Vries equation with localized noise
Yuxuan Chen, Shengquan Xiang, Zhifei Zhang +1
We establish exponential mixing for the randomly forced and weakly damped KdV equation in . The noise is bounded, localized, and degenerate in high frequencies. Ou…
Asymptotic strong Feller and weak observability inequality
Ziyu Liu, Shengquan Xiang
For a class of non-autonomous linear SPDEs, we establish the equivalence among asymptotic regularization, weak observability, and approximate null controllability for the associate…
A note on the strong Feller property via the moment method
Ziyu Liu, Shengquan Xiang
This note studies the 1D stochastic heat equation driven by a one-dimensional Brownian motion. We prove that the associated Markov process satisfies the strong Feller property unde…
Exponential mixing for the stochastic Allen--Cahn equation with localized white noise
Ziyu Liu, Shengquan Xiang, Zhifei Zhang
This paper studies the 1D stochastic Allen--Cahn equation on a bounded domain driven by localized white noise. We prove that the associated Markov process admits a unique invariant…
Exponential mixing for nonlinear Schrödinger equations perturbed by bounded degenerate noise
Yuxuan Chen, Shengquan Xiang, Zhifei Zhang
We prove the exponential convergence to a unique invariant measure for locally damped nonlinear Schrödinger equations, perturbed by bounded noise acting on only two Fourier modes.…
Donsker-Varadhan large deviation principle for locally damped and randomly forced NLS equations
Yuxuan Chen, Shengquan Xiang
We study large deviations from the invariant measure for nonlinear Schrödinger equations with colored noises on determining modes. The proof is based on a new abstract criterion,…