Transporting a Dirac Mass in a Mean Field Planning Problem
Abstract
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.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Spectral Theory in Mathematical Physics
Mathematical Biology Tumor Growth
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Volume
- 58
- Issue
- 4
- Pages
- 3622–3651
- Publication date
- 21 July 2026
- Language
- EN