Phase Analysis of a Family of Stochastic Reaction-Diffusion Equations

Abstract: We consider a wide family of reaction-diffusion equations that are forced with multiplicative space-time white noise, and show that if the level of the noise is sufficiently high then the resulting SPDE has a unique invariant measure. By contrast, we prove also that when the level of the noise is sufficiently low, then there are infinitely many invariant measures. In that case, we prove that the collection of all invariant measures is a line segment; that is, there are two extreme points. Time permitting, we will say a few thing about the two extremal invariant measures as well in the low-noise case. The phase picture that is described here was predicted in an earlier work of Zimmerman et al (2000).

This is based on joint work with Carl Mueller (University of Rochester, USA), Kunwoo Kim (POSTECH, S Korea), and Shang-Yuan Shiu (National Central University, Taiwan).

analysis of PDEsprobability

Audience: researchers in the discipline

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Stochastic PDEs and their friends

Series comments: We are organizing a three day online workshop devoted to recent developments in SPDEs and related topics. Please complete the registration form at forms.gle/G9Xw942iVNNgB4SLA if you would like to take part in the conference.

Confirmed speakers:

Yuri BAKHTIN (NYU)

Ajay CHANDRA (Imperial)

Dan CRISAN (Imperial)

Nina HOLDEN (ETH Zurich)

Kostantin KHANIN (U Toronto)

Davar KHOSHNEVISAN (University of Utah)

Nicolai KRYLOV (University of Minnesota)

Jonathan MATTINGLY (Duke)

Leonid MYTNIK (Technion)

Nicolas PERKOWSKI (Free U Berlin)

Ellen POWELL (Durham University)

Jeremy QUASTEL (U Toronto)

Daniel REMENIK (Universidad de Chile)

Armen SHIRIKYAN (University of Cergy-Pontoise)

Gigliola STAFFILANI (MIT)

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