Variational approach to stochastic porous media equations

Abstract

We shall briefly present here a different approach to stochastic porous media equations which in analogy to the variational formulation of parabolic boundary value problems will be called variational approach. It is based on a general existence result for infinite dimensional stochastic equations of the form (Formula presented) where A(t): V → V* is a family of nonlinear monotone demicontinuous operators and (V, V*) is a pair of reflexive Banach spaces with a pivot Hilbert space H.