Probabilistic representation for solutions of an irregular porous media type equation

Details Probabilistic representation for solutions of an irregular porous media type equation Probabilistic representation for solutions of an irregular porous media type equation

2008-05-15

arxiv.org/abs/0805.2383v2

Mathematics

Probability

39 pages

Scientific paper

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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