OS Stochastische Analysis: Approximate Slow Manifold for SPDEs

Tuesday, 22. March 2022
15:15 - 16:45



Prof. Dr. Dirk Blömker (Universität Augsburg)

Abstract: For a stochastic partial differential equation we approximate the infinite dimensional stochastic dynamics by the motion along a finite dimensional slow manifold. This manifold is deterministic, but not necessarily invariant for the dynamics of the unperturbed equation. Our main results are the derivation of an effective equation (given by a stochastic ordinary differential equations) on the slow manifold, and furthermore the stochastic stability of the manifold in the sense that with probability almost 1 the solution stay close to the manifold for very long times. This has applications to the motion of multiple kinks for the stochastic one-dimensional Cahn-Hilliard equation, the motion droplets in two- or three dimensional mass-conservative Allen-Cahn or Cahn-Hilliard equation, and also to travelling waves