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

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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https://hal.inria.fr/hal-00812842
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Submitted on : Friday, April 12, 2013 - 9:10:37 PM
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  • HAL Id : hal-00812842, version 1
  • ARXIV : 1304.3729

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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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