HAL - INRIA :: [inria-00410248, version 1] Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case

inria-00410248, version 1

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

Viorel Barbu ()^a^, 1, Michael Roeckner ()^b^, 2, Francesco Russo ( Auteur à contacter de préférence ) ^3, 4

(18/08/2009)

Résumé : 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.

a – University A1.I. Cuza
b – Universitaet Bielefeld
1 : Romanian Academy [IASI]
Romanian Academy of Sciences
2 : Fakultaet fuer Mathematik, SFB 701 (SFB 701)
SFB 701
3 : Laboratoire d'Analyse, Géométrie et Applications (LAGA)
CNRS : UMR7539 – Université Paris XIII - Paris Nord – Université Paris VIII - Vincennes Saint-Denis
4 : MATHFI (INRIA Rocquencourt)
INRIA – Ecole des Ponts ParisTech – Université Paris XII - Paris Est Créteil Val-de-Marne

inria-00410248, version 1
http://hal.inria.fr/inria-00410248
oai:hal.inria.fr:inria-00410248
Contributeur : Francesco Russo <>
Soumis le : Mardi 18 Août 2009, 22:22:14
Dernière modification le : Vendredi 15 Avril 2011, 16:34:10

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arXiv : 0908.2701

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