{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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Contributor : Francesco Russo <>
Submitted on : Wednesday, December 2, 2009 - 8:02:17 AM
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  • HAL Id : hal-00279975, version 2
  • ARXIV : 0805.2383

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

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