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Weak Solutions to the Stochastic Porous Media Equation via Kolmogorov Equations: The Degenerate Case

Viorel Barbu·Vladimir I. Bogachev·Giuseppe Da Prato·Michael Röckner
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Abstract

A stochastic version of the porous medium equation with coloured noise is studied. The corresponding Kolmogorov equation is solved in the space $L^2(H,ν)$ where $ν$ is an infinitesimally excessive measure. Then a weak solution is constructed.

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Viorel Barbu, Vladimir I. Bogachev, Giuseppe Da Prato, Michael Röckner. 2005-12-13. Weak Solutions to the Stochastic Porous Media Equation via Kolmogorov Equations: The Degenerate Case. https://arxiv.org/abs/math/0512266

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