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

Abstract

We consider a possibly degenerate porous media type equation over all of ℝd 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. © 2010 Springer-Verlag.