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Stochastic Generalized Porous Media and Fast Diffusion Equations

Jiagang Ren·Michael Röckner·Feng-Yu Wang
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Abstract

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 $σ$-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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Jiagang Ren, Michael Röckner, Feng-Yu Wang. 2006-02-17. Stochastic Generalized Porous Media and Fast Diffusion Equations. https://arxiv.org/abs/math/0602369

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