Title: Phase Analysis of a Family of Reaction-Diffusion Equations
Abstract: We consider a reaction-diffusion equation driven by multiplicative space-time white noise, for a large class of reaction terms that include well-known examples such as the Fisher-KPP and Allen-Cahn equations. We prove that, in the “intermittent regime”: (1) If the equation is sufficiently noisy, then the resulting stochastic PDE has a unique invariant measure; and (2) If the equation is in a low-noise regime, then there are infinitely many invariant measures and the collection of all invariant measures is a line segment in path space. This gives proof to earlier predictions of Zimmerman et al (2000), discovered first through experiments and computer simulations.
This is joint work with Carl Mueller (University of Rochester) and Kunwoo Kim (POSTECH).
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Meeting ID: 914 6737 5713