Department Mathematik



Mathematisches Kolloquium

Am Freitag, 5. Dezember 2008, um 16 Uhr c.t. spricht

Prof. Dr. Francesco Russo
(Université Paris 13)
(INRIA Rocquencourt)

im Hörsaal E27 über das Thema

Probabilistic representation of an irregular porous media type equation and related fields

Zusammenfassung: We consider a (generalized) porous media type equation over all of ${\mathbb R}^d$ with $d = 1$, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. This equation is motivated by some singular behaviour arising in complex self-organized critical systems. One of the main analytic ingredients of the proof, is a new result on uniqueness of distributional solutions of a linear PDE on ${\mathbb R}1$ with non-continuous coefficients.

This talk is based on a joint work with Ph. Blanchard and M. Röckner. Some new perspectives related with a collaboration with V. Barbu will also be mentioned.