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/