Weak Solutions to the Stochastic Porous Media Equation via Kolmogorov Equations: The Degenerate Case

Viorel Barbu; Vladimir I. Bogachev; Giuseppe Da Prato; Michael Röckner

paper

Weak Solutions to the Stochastic Porous Media Equation via Kolmogorov Equations: The Degenerate Case

arXiv:math/0512266

Abstract

A stochastic version of the porous medium equation with coloured noise is studied. The corresponding Kolmogorov equation is solved in the space $L^{2} (H, ν)$ where $ν$ is an infinitesimally excessive measure. Then a weak solution is constructed.

21 pages; BiBoS-Preprint No. 04-10-161; publication in preparation