Differential and Integral Equations

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

Ioana Ciotir and Francesco Russo

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Abstract

The purpose of this paper consists of 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.

Article information

Source
Differential Integral Equations Volume 27, Number 1/2 (2014), 181-200.

Dates
First available in Project Euclid: 12 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1384282859

Mathematical Reviews number (MathSciNet)
MR3161601

Zentralblatt MATH identifier
1313.60095

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60H30: Applications of stochastic analysis (to PDE, etc.) 60G46: Martingales and classical analysis 35C99: None of the above, but in this section

Citation

Ciotir, Ioana; Russo, Francesco. Probabilistic representation for solutions of a porous media type equation with Neumann boundary condition: The case of the half-line. Differential Integral Equations 27 (2014), no. 1/2, 181--200. https://projecteuclid.org/euclid.die/1384282859.


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