A Hyperbolic–parabolic framework to manage traffic generated pollution

Abstract

Vehicular traffic flows through a merge regulated by traffic lights and produces pollutant that diffuses in the surrounding region. This situation motivates a general hyperbolic - parabolic system, whose well-posedness and stability are here proved in $L^1$. Roads are allowed to be also 2-dimensional. The effects of stop & go waves are comprised, leading to measure source terms in the parabolic equation. The traffic lights, as well as inflows and outflows, can be regulated to minimize the presence of pollutant in given regions.