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 random nonlinear wave equations: weak dissipation and localized control
4 Pith papers cite this work. Polarity classification is still indexing.
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2026 4verdicts
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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.
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.
Proves the strong Feller property for the Markov process of the 1D stochastic heat equation using Malliavin calculus combined with the moment method.
citing papers explorer
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Exponential mixing for nonlinear Schr\"odinger equations perturbed by bounded degenerate noise
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.