Transporting a Dirac mass in a mean field planning problem
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866912813053640704 |
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| 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 |