In this paper, we introduce a dynamical urban planning model. This leads to the study of a system of nonlinear equations coupled through multi-marginal optimal transport problems. A first example consists in solving two equations coupled through the solution to the Monge–Ampère equation. We show that theWasserstein gradient flow theory provides a very good framework to solve these highly nonlinear systems. At the end, a uniqueness result is presented in dimension one based on convexity arguments.

中文翻译：

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通过多边际传输问题耦合的非线性系统

在本文中，我们介绍了一个动态的城市规划模型。这导致了对通过多边际最优传输问题耦合的非线性方程组的研究。第一个示例包括求解两个通过 Monge-Ampère 方程的解耦合的方程。我们表明，Wasserstein 梯度流理论为解决这些高度非线性系统提供了一个很好的框架。最后，基于凸性参数在维度一中呈现唯一性结果。