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arXiv · 0805.2383

Probabilistic representation for solutions of an irregular porous media type equation

Philippe Blanchard·Michael Röckner·Francesco Russo
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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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Philippe Blanchard, Michael Röckner, Francesco Russo. 2009-12-02. Probabilistic representation for solutions of an irregular porous media type equation. https://arxiv.org/abs/0805.2383

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