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

Viorel Barbu, Michael Röckner and Francesco Russo
septembre, 2011
Publication type:
Paper in peer-reviewed journals
Journal:
Probability Theory and Related Fields, vol. 151, 1-2, pp. 1-43
Publisher:
Springer
arXiv:
images/icons/icon_arxiv.png 0908.2701
Keywords :
Singular degenerate porous media type equation – Probabilistic representation
Abstract:
We consider a possibly degenerate porous media type equation over all of {\mathbb 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.
BibTeX:
@article{Bar-Roc-Rus-2011,
    author={Viorel Barbu and Michael Röckner and Francesco Russo },
    title={Probabilistic representation for solutions of an irregular 
           porous media type equation: the degenerate case. },
    doi={10.1007/s00440-010-0291-x },
    journal={Probability Theory and Related Fields },
    year={2011 },
    month={9},
    volume={151, 1-2 },
    pages={1--43},
}