On a class of stochastic partial differential equations with multiple invariant measures

@article{Farkas2021OnAC,
title={On a class of stochastic partial differential equations with multiple invariant measures},
author={B{\'a}lint Farkas and Martin Friesen and Barbara R{\"u}diger and Dennis Schroers},
journal={Nonlinear Differential Equations and Applications NoDEA},
year={2021},
volume={28}
}
• Published 4 May 2020
• Mathematics
• Nonlinear Differential Equations and Applications NoDEA
In this work we investigate the long-time behavior for Markov processes obtained as the unique mild solution to stochastic partial differential equations in a Hilbert space. We analyze the existence and characterization of invariant measures as well as convergence of transition probabilities. While in the existing literature typically uniqueness of invariant measures is studied, we focus on the case where the uniqueness of invariant measures fails to hold. Namely, introducing a generalized…
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