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

january, 2014
Publication type:
Paper in peer-reviewed journals
Journal:
Differential and Integral Equations. Advances in Differential Equations., vol. 27 1/2, pp. 181-200
arXiv:
images/icons/icon_arxiv.png 1304.3729
Keywords :
stochastic differential equations; reflection; porous media type equation; probabilistic representation.
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.
BibTeX:
@article{Cio-Rus-2014,
    author={Ioana Ciotir and Francesco Russo },
    title={Probabilistic representation for solutions of a porous media 
           type equation with Neumann boundary condition: the case of the 
           half-line. },
    journal={Differential and Integral Equations. Advances in Differential 
           Equations. },
    year={2014 },
    month={1},
    volume={27 1/2 },
    pages={181--200},
}