Mathematical Study of Reaction-Diffusion in Congested Crowd Motion

Abstract

This paper establishes existence, uniqueness, and an L^1-comparison principle for weak solutions of a PDE system modeling phase transition reaction-diffusion in congested crowd motion. We consider a general reaction term and mixed homogeneous (Dirichlet and Neumann) boundary conditions. This model is applicable to various problems, including multi-species diffusion-segregation and pedestrian dynamics with congestion. Furthermore, our analysis of the reaction term yields sufficient conditions combining the drift with the reaction that guarantee the absence of congestion, reducing the dynamics to a constrained linear reaction-transport equation.