Stochastic Generalized Porous Media and Fast Diffusion Equations

Details Stochastic Generalized Porous Media and Fast Diffusion Equations Stochastic Generalized Porous Media and Fast Diffusion Equations

2006-02-17

arxiv.org/abs/math/0602369v1

Mathematics

Probability

36 pages, BiBoS-Preprint No. 06-02-205

Scientific paper

We present a generalization of Krylov-Rozovskii's result on the existence and uniqueness of solutions to monotone stochastic differential equations. As an application, the stochastic generalized porous media and fast diffusion equations are studied for $\sigma$-finite reference measures, where the drift term is given by a negative definite operator acting on a time-dependent function, which belongs to a large class of functions comparable with the so-called $N$-functions in the theory of Orlicz spaces.

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