Stability of large-amplitude traveling fronts for a traffic flow model with moving barriers

Abstract

In this paper, we study the existence and stability of traveling front solutions to a nonlinear hyperbolic system of balance law, which models the dynamics of a heterogeneous traffic flow with moving barriers (e.g. slow vehicles). We first prove via shooting method that, the balance law admits a family of monotone traveling fronts, if the barriers have small strength regardless of their shapes. Then we show that, under some assumptions on the nonlinearities and by applying detailed spectral analysis and $ C_0 $ semigroup theories, the traveling fronts are spectrally stable, linearly and nonlinearly exponentially stable in some exponentially weighted spaces, where the wave strengths can be large.