| Autor: |
Ambrosio, Luigi, Baradat, Aymeric, Brenier, Yann |
| Rok vydání: |
2020 |
| Předmět: |
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| Zdroj: |
Analysis & PDE 16 (2023) 2005-2040 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.2140/apde.2023.16.2005 |
| Popis: |
Monge-Amp\`ere gravitation is a modification of the classical Newtonian gravitation where the linear Poisson equation is replaced by the nonlinear Monge-Amp\`ere equation. This paper is concerned with the rigorous derivation of Monge-Amp\`ere gravitation for a finite number of particles from the stochastic model of a Brownian point cloud, in the spirit of a previous work by the third author [A double large deviation principle for Monge-Amp\`ere gravitation, 2016]. The main step in this derivation is the $\Gamma-$convergence of the good rate functions corresponding to a one-parameter family of large deviation principles. Surprisingly, the derived model includes dissipative phenomena. As an illustration, we show that it leads to sticky collisions in one space dimension. |
| Databáze: |
arXiv |
| Externí odkaz: |
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