Uniqueness and stability with respect to parameters of solutions to a fluid-like driven system for active-passive pedestrian dynamics

Abstract

We study a system of parabolic equations consisting of a double nonlinear parabolic equations of Forchheimer type coupled with a semilinear parabolic equations. The system describes a fluid-like driven system for active-passive pedestrian dynamics. The structure of the nonlinearity of the coupling allows us to prove the uniqueness of solutions. We provide also stability estimates of solutions with respect to selected parameters.

19 pages