Probabilistic representation for solutions of an irregular porous media type equation
Philippe Blanchard, Michael Röckner, and Francesco Russo
Source: Ann. Probab. Volume 38, Number 5
(2010), 1870-1900.
Abstract
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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Keywords: Singular porous media type equation; probabilistic representation; self-organized criticality (SOC)
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Permanent link to this document: http://projecteuclid.org/euclid.aop/1282053774
Digital Object Identifier: doi:10.1214/10-AOP526
Zentralblatt MATH identifier: 05793424
Mathematical Reviews number (MathSciNet): MR2722788
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