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Journal Articles Probability Theory and Related Fields Year : 2011

Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case

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Abstract

We consider a possibly degenerate 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. The main idea consists in approximating the equation by equations with monotone non-degenerate coefficients and deriving some new analytical properties of the solution.
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Dates and versions

inria-00410248 , version 1 (18-08-2009)

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Viorel Barbu, Michael Roeckner, Francesco Russo. Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case. Probability Theory and Related Fields, 2011, ⟨10.1007/s00440-010-0291-x⟩. ⟨inria-00410248⟩
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