# A probabilistic algorithm approximating solutions of a singular PDE of porous media type

* Corresponding author
3 MATHFI - Financial mathematics
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech, UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12
Abstract : The object of this paper is a one-dimensional generalized porous media equation (PDE) with possibly discontinuous coefficient $\beta$, which is well-posed as an evolution problem in $L^1(\mathbb{R})$. In some recent papers of Blanchard et alia and Barbu et alia, the solution was represented by the solution of a non-linear stochastic differential equation in law if the initial condition is a bounded integrable function. We first extend this result, at least when $\beta$ is continuous and the initial condition is only integrable with some supplementary technical assumption. The main purpose of the article consists in introducing and implementing a stochastic particle algorithm to approach the solution to (PDE) which also fits in the case when $\beta$ is possibly irregular, to predict some long-time behavior of the solution and in comparing with some recent numerical deterministic techniques.
Keywords :
Document type :
Preprints, Working Papers, ...
Domain :

Cited literature [51 references]

https://hal.inria.fr/inria-00535806
Contributor : Francesco Russo Connect in order to contact the contributor
Submitted on : Friday, November 12, 2010 - 6:59:05 PM
Last modification on : Tuesday, October 19, 2021 - 4:06:44 PM
Long-term archiving on: : Sunday, February 13, 2011 - 2:51:23 AM

### Files

MainBCRSentNov2010.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : inria-00535806, version 1
• ARXIV : 1011.3107

### Citation

Nadia Belaribi, François Cuvelier, Francesco Russo. A probabilistic algorithm approximating solutions of a singular PDE of porous media type. 2010. ⟨inria-00535806⟩

Record views