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arXiv · 0908.2701

Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case

Viorel Barbu·Michael Roeckner·Francesco Russo
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Abstract

We consider a possibly degenerate porous media type equation over all of $\R^d$ with $d = 1$, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. This equation is motivated by some singular behaviour arising in complex self-organized critical systems. The main idea consists in approximating the equation by equations with monotone non-degenerate coefficients and deriving some new analytical properties of the solution.

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Viorel Barbu, Michael Roeckner, Francesco Russo. 2009-08-19. Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case. https://doi.org/10.1007/s00440-010-0291-x

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