Margaret Beck: Understanding metastability using invariant manifolds

Margaret Beck, Boston University

Time: Wed 2010-03-03 16.00

Location: Room 3721, Department of mathematics, KTH, Lindstedtsvägen 25, 7th floor

Metastability refers to transient dynamics that persist for long times. More precisely, suppose a PDE has a globally attracting state, meaning that, for any initial condition, the solution will asymptotically approach that state. It can happen that, on its way to the state, the solution spends a long period of time near another, possibly unstable, state. This happens, for example, in the Navier-Stokes equation in two spatial dimensions and Burgers equation in one spatial dimension, both with small viscosity. I will explain how, in the context of Burgers equation, this behavior can be understood using certain global invariant manifolds in the phase space of the PDE.

Coffee is served in the lunch room at 15.30.