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Existence and Uniqueness of Nonnegative Solutions to the Stochastic Porous Media Equation

Viorel Barbu·Giuseppe Da Prato·Michael Röckner
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Abstract

One proves that the stochastic porous media equation in 3-D has a unique nonnegative solution for nonnegative initial data in $H^{-1}(\mathcal O)$ if the nonlinearity is monotone and has polynomial growth.

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Viorel Barbu, Giuseppe Da Prato, Michael Röckner. 2007-03-14. Existence and Uniqueness of Nonnegative Solutions to the Stochastic Porous Media Equation. https://arxiv.org/abs/math/0703420

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