  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.
