# {Probabilistic representation for solutions of an irregular porous media type equation.

Abstract : We consider a 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. One of the main analytic ingredients of the proof, is a new result on uniqueness of distributional solutions of a linear PDE on $\R^1$ with non-continuous coefficients.
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Cited literature [31 references]

https://hal.archives-ouvertes.fr/hal-00279975
Contributor : Francesco Russo <>
Submitted on : Wednesday, December 2, 2009 - 8:02:17 AM
Last modification on : Saturday, February 15, 2020 - 2:04:39 AM
Long-term archiving on: Thursday, September 23, 2010 - 11:10:34 AM

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### Identifiers

• HAL Id : hal-00279975, version 2
• ARXIV : 0805.2383

### Citation

Philippe Blanchard, Michael Röckner, Francesco Russo. {Probabilistic representation for solutions of an irregular porous media type equation.. 2009. ⟨hal-00279975v2⟩

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