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

Ioana Ciotir; Francesco Russo

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arXiv · 1304.3729

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

Ioana Ciotir·Francesco Russo

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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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BibTeX RIS

Ioana Ciotir, Francesco Russo. 2013-04-12. Probabilistic representation for solutions of a porous media type equation with Neumann boundary condition: the case of the half-line. https://arxiv.org/abs/1304.3729

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