Exponential mixing for random nonlinear wave equations: weak dissipation and localized control

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• Exponential mixing for the stochastic Allen--Cahn equation with localized white noise math.PR · 2026-05-07 · unverdicted · none · ref 40

  The 1D stochastic Allen-Cahn equation with localized white noise admits a unique invariant measure and its Markov process is exponentially mixing.

• Exponential mixing for nonlinear Schr\"odinger equations perturbed by bounded degenerate noise math.AP · 2026-04-07 · unverdicted · none · ref 39

  Exponential mixing to a unique invariant measure is established for locally damped NLS with bounded degenerate noise on two modes using a new criterion based on asymptotic compactness of the linearized system.

• Stability for the stochastic heat equation with multiplicative noise via finite-dimensional feedback math.OC · 2026-04-09 · unverdicted · none · ref 27

  Finite-dimensional Fourier-mode feedback stabilizes the stochastic heat equation with multiplicative noise in both mean-square and almost sure senses, yielding explicit decay rates and a new controllability proof.

• A note on the strong Feller property via the moment method math.PR · 2026-05-26 · unverdicted · none · ref 20

  Proves the strong Feller property for the Markov process of the 1D stochastic heat equation using Malliavin calculus combined with the moment method.