seminar: Stochastic porous media and fast diffusion equations
speaker: Michael Röckner (Faculty of Mathematics, Bielefeld University)abstract: We first present a new existence and uniqueness result for stochastic evolution equations on Hilbert spaces. This is a generalization of a classical result by Krylov and Rozovskii based on the so-called variational approach to stochastic partial differential equations (SPDE). The main motivation are applications to nonlinear SPDE of porous media type which also include cases where the nonlinear functions grow slowly at infinity ("fast diffusion equations"). Generally, the main problem is to find the appropriate Gelfand triple to work on. In our case Orlics spaces turn out to be convenient. We show how one must choose the defining Young function for a given nonlinearity. After presenting these applications, we shall summarize results about the qualitative behaviour of solutions and about their invariant measures.
timetable:
Fri 9 Jun, 11:40 - 12:20, Aula Mancini
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