Stochastic generalized porous media and fast diffusion equations

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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. © 2007.

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Ren, J., Röckner, M., & Wang, F. Y. (2007). Stochastic generalized porous media and fast diffusion equations. Journal of Differential Equations, 238(1), 118–152. https://doi.org/10.1016/j.jde.2007.03.027

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