A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts
Analysis of PDEs
2016-06-16 v1
Abstract
We prove an existence result for nonlinear diffusion equations in the presence of a nonlocal density-dependent drift which is not necessarily potential. The proof is constructive and based on the Helmholtz decomposition of the drift and a splitting scheme. The splitting scheme combines transport steps by the divergence-free part of the drift and semi-implicit minimization steps \`a la Jordan-Kinderlherer-Otto to deal with the potential part.
Cite
@article{arxiv.1606.04793,
title = {A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts},
author = {Guillaume Carlier and Maxime Laborde},
journal= {arXiv preprint arXiv:1606.04793},
year = {2016}
}