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The object of this paper is a one-dimensional generalized porous mediaequation (PDE) with possibly discontinuous coefficient $\beta$, which iswell-posed as an evolution problem in $L^1(\mathbb{R})$. In some recent papersof Blanchard et alia and Barbu et alia, the solution was represented by thesolution of a non-linear stochastic differential equation in law if the initialcondition is a bounded integrable function. We first extend this result, atleast when $\beta$ is continuous and the initial condition is only integrablewith some supplementary technical assumption. The main purpose of the articleconsists in introducing and implementing a stochastic particle algorithm toapproach the solution to (PDE) which also fits in the case when $\beta$ ispossibly irregular, to predict some long-time behavior of the solution and incomparing with some recent numerical deterministic techniques.

A probabilistic algorithm approximating solutions of a singular PDE of porous media type