Solvability of a coupled nonlinear system of Skorohod like stochastic differential equations modeling active passive pedestrians dynamics through a heterogeneous domain and fire
We study the existence and uniqueness of solutions to a coupled nonlinear system of Skorohod like stochastic differential equations with reflecting boundary condition. The setting describes the evacuation dynamics of a mixed crowd composed of both active and passive pedestrians moving through a domain with obstacles, fire and smoke. As main working techniques, we use compactness methods and the Skorohod's representation of solutions to SDEs posed in bounded domains. The challenge is to handle the coupling and the nonlinearities present in the model equations together with the multiple connectedness of the domain and the pedestrian obstacle interaction.