Probabilistic approximation for a porous medium equation

In this paper, we are interested in the one-dimensional porous medium equation when the initial condition is the distribution function of a probability measure. We associate a nonlinear martingale problem with it. After proving uniqueness for the martingale problem, we show existence owing to a propagation of chaos result for a system of weakly interacting diffusion processes. The particle system obtained by increasing reordering from these diffusions is proved to solve a stochastic differential equation with normal reflection. Last, we obtain propagation of chaos for the reordered particles to a probability measure which does not solve the martingale problem but is also linked to the porous medium equation.