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{Probabilistic representation for solutions of an irregular porous media type equation.

Abstract

We consider a porous media type equation over all of $\R^d$ 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. 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.
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Dates and versions

hal-00279975 , version 1 (15-05-2008)
hal-00279975 , version 2 (02-12-2009)

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Cite

Philippe Blanchard, Michael Röckner, Francesco Russo. {Probabilistic representation for solutions of an irregular porous media type equation.. 2009. ⟨hal-00279975v2⟩
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