Existence and uniqueness of nonnegative solutions to the stochastic porous media equation Viorel BarbuGiuseppe Da PratoMichael Roeckner 76S0560H15porous media equationstochastic PDEsYosida approximation 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. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3241 10.1512/iumj.2008.57.3241 en Indiana Univ. Math. J. 57 (2008) 187 - 212 state-of-the-art mathematics http://iumj.org/access/