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

TL;DR

This paper analyzes a coupled nonlinear parabolic system modeling active-passive pedestrian dynamics, establishing solution uniqueness and stability with respect to system parameters.

Contribution

It introduces a novel coupled parabolic model for pedestrian dynamics and proves solution uniqueness and stability based on the system's nonlinear structure.

Findings

Proved uniqueness of solutions for the model.

Derived stability estimates relative to parameters.

Established well-posedness of the system.

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.