Probabilistic representation for solutions of a porous media type equation with Neumann boundary condition: the case of the half-line. - Archive ouverte HAL Access content directly
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Probabilistic representation for solutions of a porous media type equation with Neumann boundary condition: the case of the half-line.

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Ioana Ciotir
Francesco Russo

Abstract

The purpose of this paper consists in proposing a generalized solution for a porous media type equation on a half-line with Neumann boundary condition and prove a probabilistic representation of this solution in terms of an associated microscopic diffusion. The main idea is to construct a stochastic differential equation with reflection which has a solution in law and whose marginal law densities provide the unique solution of the porous media type equation.
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hal-00812842 , version 1 (12-04-2013)

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Ioana Ciotir, Francesco Russo. Probabilistic representation for solutions of a porous media type equation with Neumann boundary condition: the case of the half-line.. 2013. ⟨hal-00812842⟩
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