IUMJ

Title: Existence and uniqueness of nonnegative solutions to the stochastic porous media equation

Authors: Giuseppe Da Prato, Viorel Barbu and Michael Roeckner

Issue: Volume 57 (2008), Issue 1, 187-212

Abstract:

It is proved that the stochastic porous media equation in a bounded domain $\mathcal{O}$ of $\mathbb{R}^{3}$, with multiplicative noise, with a monotone nonlinearity of polynomial growth has a unique nonnegative solution in $H^{-1}(\mathcal{O})$ (in particular is nonnegative measure-valued), provided the initial data is in $H^{-1}(\mathcal{O})$ and nonnegative.