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arXiv · 2506.16041

Transporting a Dirac mass in a mean field planning problem

Pierre Cardaliaguet·Sebastian Munoz·Alessio Porretta
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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 $0$. We proceed by studying a continuous rescaling of the solution, and characterizing its behavior near the initial time through an appropriate Lyapunov functional.

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Pierre Cardaliaguet, Sebastian Munoz, Alessio Porretta. 2025-06-19. Transporting a Dirac mass in a mean field planning problem. https://arxiv.org/abs/2506.16041

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