Nonlinear systems coupled through multi-marginal transport problems

Maxime Laborde

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arXiv · 1805.01331

Nonlinear systems coupled through multi-marginal transport problems

Maxime Laborde

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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.

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Maxime Laborde. 2018-05-03. Nonlinear systems coupled through multi-marginal transport problems. https://arxiv.org/abs/1805.01331

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