Unique ergodicity for a class of stochastic hyperbolic equations with additive space-time white noise

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

In this paper, we consider a certain class of second order nonlinear PDEs with damping and space-time white noise forcing, posed on the d-dimensional torus. This class includes the wave equation for d=1 and the beam equation for d≤3. We show that the Gibbs measure is the unique invariant measure for this system. Since the flow does not satisfy the strong Feller property, we introduce a new technique for showing unique ergodicity. This approach may be also useful in situations in which finite-time blowup is possible.
Original languageEnglish
Pages (from-to)1311-1347
Number of pages37
JournalCommunications in Mathematical Physics
Volume377
Early online date7 May 2020
DOIs
Publication statusPublished - 31 Jul 2020

Fingerprint

Dive into the research topics of 'Unique ergodicity for a class of stochastic hyperbolic equations with additive space-time white noise'. Together they form a unique fingerprint.

Cite this