Probabilistic representation for solutions of an irregular porous media type equation

Philippe Blanchard, Röckner Michael and Francesco Russo
2010
Publication type:
Paper in peer-reviewed journals
Journal:
Annals of Probability, vol. 38, 5, pp. 1870–1900
arXiv:
images/icons/icon_arxiv.png 0805.2383
Keywords :
Singular porous media type equation,probabilistic representation, self-organized criticality (SOC).
Abstract:
We consider a porous media type equation over all of $\R^d$ with $d = 1$, with monotone discontinuous coefficient 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 interest in such a singular porous media equations is due to the fact that they can model systems exhibiting the phenomenon of self-organized criticality. 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.
BibTeX:
@article{Bla-Roc-Rus-2010,
    author={Philippe Blanchard and Röckner Michael and Francesco Russo },
    title={Probabilistic representation for solutions of an irregular 
           porous media type equation },
    doi={10.1214/10-AOP526 },
    journal={Annals of Probability },
    year={2010 },
    volume={38, 5 },
    pages={1870–1900},
}