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 ${\mathbb{R}}^d$ 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.

References in corpus (1)

• Stochastic Porous Media Equation and Self-Organized Criticality

Cited by in corpus (1)

• Existence and uniqueness results for time-inhomogeneous time-change equations and Fokker--Planck equations