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The purpose of this paper consists in proposing a generalized solution for aporous media type equation on a half-line with Neumann boundary condition andprove a probabilistic representation of this solution in terms of an associatedmicroscopic diffusion. The main idea is to construct a stochastic differentialequation with reflection which has a solution in law and whose marginal lawdensities provide the unique solution of the porous media type equation.

Probabilistic representation for solutions of a porous media type equation with Neumann boundary condition: the case of the half-line