Gradient flows driven by a non-smooth repulsive interaction potential
Analysis of PDEs
2013-10-15 v1
Abstract
This thesis analyze the Wasserstein gradient flow of a functional defined as a double convolution of a non-smooth repulsive interaction potential. To be more precise, the potential under investigation has a -|x| behavior close to the origin. The already existent machinery of Wasserstein gradient flow is well posed for lambda-convex potential. In this case this property is lost, but it is proven that in the one dimensional case existence and uniqueness of the solution is still achieved.
Keywords
Cite
@article{arxiv.1310.3677,
title = {Gradient flows driven by a non-smooth repulsive interaction potential},
author = {Giovanni A. Bonaschi},
journal= {arXiv preprint arXiv:1310.3677},
year = {2013}
}