Recent extinction results for stochastic porous media equations and applications to self-organized criticality

Datum

28.10.2011

Zeit

11:10 - 12:10

Sprecher

Prof. Dr. Michael Röckner

Zugehörigkeit

Universität Bielefeld

Serie

TUD Mathematik AG Analysis & Stochastik

Sprache

en

Hauptthema

Mathematik

Andere Themen

Mathematik

Beschreibung

The rst part of the talk will recall extinction results for stochastic partial differential equations (with multiplicative noise) of porous media type. These include stochastic fast diusion equations and more singular cases, where e.g. the nonlinearity is given by a Heaviside or sign function, so is multivalued. The latter describe certain continuum models for the phenomenon of self-organized criticality (SOC). These extinction results have been obtained in the past two years. In the SOC-case, however, extinction was only shown if the underlying spatial domain is one-dimensional and only with positive though high) probability. The second part of the talk is devoted to very recent results, where for the OC-case asymptotic extinction was proved for all spatial dimensions and shown to be locally xponentially fast. One main technique in the proofs is to transform the stochastic PDE into a deterministic PDE with a random parameter. The resulting deterministic PDE is of an entirely new type nd new methods had to be invented for its analysis.

Letztmalig verändert: 28.10.2011, 11:58:08