Conservation laws with discontinuous flux

Abstract

We consider a hyperbolic conservation law with discontinuous flux. Such a partial differential equation arises in different applications, in particu- lar we are motivated by a model of traffic flow. We provide a new formulation in terms of Riemann Solvers. Moreover, we determine the class of Riemann Solvers which provide existence and uniqueness of the corresponding weak en- tropic solutions

Existence results for Hughes' model for pedestrian flows

“…Line (4b) comes from the boundary condition introduced by Bardos et al in [6], see also [4,8,9,19]. The latter line (4c) accounts for the discontinuity of the flux along the turning curve, see [1,3,5,14,21].…”

ADER schemes and high order coupling on networks of hyperbolic conservation laws

“…If there have been no computations before we fill the ghost cells with data obtained by a one sided reconstruction presented in [30]. If the computations from time step t l are available, we can simply use the polynomial (13). In the previous update it was used to describe the Godunov state at the junction during the period [t l , t l+1 ].…”

“…Networks of hyperbolic conservation laws occur in many applications such as the human circulatory system [1,2,3,4], gas pipelines [5,6,7], water [8,9,10,11] and road networks [12,13]. For all these applications accurate and stable numerical methods are needed.…”

Nash equilibria for a model of traffic flow with several groups of drivers

“…Various optimization problems for traffic flow, based on the Lighthill-Whitham conservation law model, have been considered in [8,9,10,11]. For an introduction to differential games and for recent applications to traffic flow on networks we refer to [6] and [7], respectively.…”