On abstract Barenblatt equations
نویسندگان
چکیده
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.
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