Transporting a Dirac mass in a mean field planning problem

Fuente: arXiv
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Main Authors: Cardaliaguet, Pierre, Munoz, Sebastian, Porretta, Alessio
Format: Preprint
Published: 2025
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_version_ 1866912813053640704
author Cardaliaguet, Pierre
Munoz, Sebastian
Porretta, Alessio
author_facet Cardaliaguet, Pierre
Munoz, Sebastian
Porretta, Alessio
contents 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 $0$. We proceed by studying a continuous rescaling of the solution, and characterizing its behavior near the initial time through an appropriate Lyapunov functional.
format Preprint
id arxiv_https___arxiv_org_abs_2506_16041
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Transporting a Dirac mass in a mean field planning problem
Cardaliaguet, Pierre
Munoz, Sebastian
Porretta, Alessio
Analysis of PDEs
35R35, 35Q89, 35B65, 35J70
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 $0$. We proceed by studying a continuous rescaling of the solution, and characterizing its behavior near the initial time through an appropriate Lyapunov functional.
title Transporting a Dirac mass in a mean field planning problem
topic Analysis of PDEs
35R35, 35Q89, 35B65, 35J70
url https://arxiv.org/abs/2506.16041