Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case - Archive ouverte HAL Access content directly
Journal Articles Probability Theory and Related Fields Year : 2011

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

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Viorel Barbu
• Function : Author
• PersonId : 862682
Michael Roeckner
• Function : Author
• PersonId : 862683
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.

#### Domains

Mathematics [math] Probability [math.PR]

### Dates and versions

inria-00410248 , version 1 (18-08-2009)

### Identifiers

• HAL Id : inria-00410248 , version 1
• ARXIV :
• DOI :

### Cite

Viorel Barbu, Michael Roeckner, Francesco Russo. Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case. Probability Theory and Related Fields, 2011, ⟨10.1007/s00440-010-0291-x⟩. ⟨inria-00410248⟩

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