Nonlinear systems coupled through multi-marginal transport problems
Analysis of PDEs
2018-05-04 v1
Abstract
In this paper, we introduce a dynamical urban planning model. This leads us to study a system of nonlinear equations coupled through multi-marginal optimal transport problems. A simple case consists in solving two equations coupled through the solution to the Monge-Amp{\`e}re equation. We show that the Wasserstein gradient flow theory provides a very good framework to solve this highly nonlinear system. At the end, an uniqueness result is presented in dimension one based on convexity arguments.
Keywords
Cite
@article{arxiv.1805.01331,
title = {Nonlinear systems coupled through multi-marginal transport problems},
author = {Maxime Laborde},
journal= {arXiv preprint arXiv:1805.01331},
year = {2018}
}