Derivation of the fractional porous medium equation from a microscopic dynamics
Probability
2023-02-22 v2 Analysis of PDEs
Abstract
In this article we derive the fractional porous medium equation for any power of the fractional Laplacian as the hydrodynamic limit of a microscopic dynamics of random particles with long range interactions, but the jump rate highly depends on the occupancy near the sites where the interactions take place.
Keywords
Cite
@article{arxiv.2205.00812,
title = {Derivation of the fractional porous medium equation from a microscopic dynamics},
author = {Pedro Cardoso and Renato De Paula and Patrícia Gonçalves},
journal= {arXiv preprint arXiv:2205.00812},
year = {2023}
}