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September 2010 Probabilistic representation for solutions of an irregular porous media type equation
Philippe Blanchard, Michael Röckner, Francesco Russo
Ann. Probab. 38(5): 1870-1900 (September 2010). DOI: 10.1214/10-AOP526


We consider a porous media type equation over all of ℝd, 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 ℝ1 with not necessarily continuous coefficients.


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Philippe Blanchard. Michael Röckner. Francesco Russo. "Probabilistic representation for solutions of an irregular porous media type equation." Ann. Probab. 38 (5) 1870 - 1900, September 2010.


Published: September 2010
First available in Project Euclid: 17 August 2010

zbMATH: 1202.60111
MathSciNet: MR2722788
Digital Object Identifier: 10.1214/10-AOP526

Primary: 35C99 , 58J65 , 60G46 , 60H10 , 60H30

Keywords: probabilistic representation , self-organized criticality (SOC) , Singular porous media type equation

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 5 • September 2010
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