In this paper we are interested in abstract problems of Barenblatt's type. In a first part, we investigate the problem f (∂ t u) + Au = g where f and A are maximal monotone operators and by assuming that A derives from a potential J. With general assumptions on the operators, we prove the existence of a solution. In the second part of the paper, we examine a stochastic version of the above problem: f [∂ t (u − t 0 hdw)] + Au = 0 , with some restrictive assumptions on the data due principally to the framework of the Itô integral.