Transporting a Dirac mass in a mean field planning problem
Analysis of PDEs
2026-01-13 v2
Abstract
We study a mean field planning problem in which the initial density is a Dirac mass. We show that there exists a unique solution which converges to a self-similar profile as time tends to . We proceed by studying a continuous rescaling of the solution, and characterizing its behavior near the initial time through an appropriate Lyapunov functional.
Cite
@article{arxiv.2506.16041,
title = {Transporting a Dirac mass in a mean field planning problem},
author = {Pierre Cardaliaguet and Sebastian Munoz and Alessio Porretta},
journal= {arXiv preprint arXiv:2506.16041},
year = {2026}
}