Weak solutions to stochastic porous media equations

Da Prato G, Röckner M. Weak solutions to stochastic porous media equations. Journal of Evolution Equations. 2004;4(2):249-271.A stochastic version of the porous medium equation is studied. The corresponding Kolmogorov equation is solved in a space L-2 (H, v) where v is an invariant measure. Then a weak solution, that is a solution in the sense of the corresponding martingale problem, is constructed