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
External link:
HAL:
arXiv:
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},
}