Orateur
Description
We introduce a new class of cross-diffusion systems for the macroscopic description of congested motion in interacting populations. The model is derived from a transport–correction algorithm: a transport step accounts for the individuals' desired motion, while a correction governed by a minimum-flow principle enforces congestion constraints. Compared with Wasserstein-based formulations, this approach yields a different mobility structure and provides a variational framework for establishing existence and uniqueness. We present well-posedness results under suitable assumptions, allowing mixed Dirichlet–Neumann boundary conditions to represent exits and impermeable walls. Numerical simulations in selected configurations illustrate the resulting dynamics.