Probabilistic representation for solutions of an irregular porous media type equation

Blanchard P, Röckner M, Russo F (2010)
The Annals of Probability 38(5): 1870-1900.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Blanchard, PhilippeUniBi; Röckner, Michael; Russo, Francesco
Abstract / Bemerkung
We consider a porous media type equation over all of R-d, d = 1, with monotone discontinuous coefficient with linear growth, and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. The interest in such 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 not necessarily continuous coefficients.
Stichworte
Singular porous media type equation; self-organized criticality (SOC); probabilistic representation
Erscheinungsjahr
2010
Zeitschriftentitel
The Annals of Probability
Band
38
Ausgabe
5
Seite(n)
1870-1900
ISSN
0091-1798
Page URI
https://pub.uni-bielefeld.de/record/1794071

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Blanchard P, Röckner M, Russo F. Probabilistic representation for solutions of an irregular porous media type equation. The Annals of Probability. 2010;38(5):1870-1900.
Blanchard, P., Röckner, M., & Russo, F. (2010). Probabilistic representation for solutions of an irregular porous media type equation. The Annals of Probability, 38(5), 1870-1900. doi:10.1214/10-AOP526
Blanchard, P., Röckner, M., and Russo, F. (2010). Probabilistic representation for solutions of an irregular porous media type equation. The Annals of Probability 38, 1870-1900.
Blanchard, P., Röckner, M., & Russo, F., 2010. Probabilistic representation for solutions of an irregular porous media type equation. The Annals of Probability, 38(5), p 1870-1900.
P. Blanchard, M. Röckner, and F. Russo, “Probabilistic representation for solutions of an irregular porous media type equation”, The Annals of Probability, vol. 38, 2010, pp. 1870-1900.
Blanchard, P., Röckner, M., Russo, F.: Probabilistic representation for solutions of an irregular porous media type equation. The Annals of Probability. 38, 1870-1900 (2010).
Blanchard, Philippe, Röckner, Michael, and Russo, Francesco. “Probabilistic representation for solutions of an irregular porous media type equation”. The Annals of Probability 38.5 (2010): 1870-1900.