Convergence of rough Follow-the-Leader approximations and existence of weak solutions for the one-dimensional Hughes model

Hyperbolic conservation laws (35L65) Theoretical approximation in context of PDEs (35A35) Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics (82B21) Initial value problems for first-order hyperbolic equations (35L03) Traffic and pedestrian flow models (76A30)

Cites Work

On the micro-to-macro limit for first-order traffic flow models on networks
Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic
On entropy weak solutions of Hughes' model for pedestrian motion
On the micro-macro limit in traffic flow
A traffic flow model with non-smooth metric interaction: well-posedness and micro-macro limit
On the time continuity of entropy solutions
A theory of \(L ^{1}\)-dissipative solvers for scalar conservation laws with discontinuous flux
Deterministic particle approximation of the Hughes model in one space dimension
Convergence of approximate solutions to conservation laws
The continuum limit of follow-the-leader models -- a short proof
Deterministic particle approximation of scalar conservation laws
Convergence of the Lax-Friedrichs scheme and stability for conservation laws with a discontinuous space-time dependent flux
Follow-the-leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow
Traveling wave profiles for a follow-the-leader model for traffic flow with rough road condition
Nonlinear Follow-the-Leader Models of Traffic Flow
Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems
Convergence of a Difference Scheme for Conservation Laws with a Discontinuous Flux
Resurrection of "Second Order" Models of Traffic Flow
Micro-Macro Limit of a Nonlocal Generalized Aw-Rascle Type Model
Shock Waves on the Highway
A 2-Phase Traffic Model Based on a Speed Bound
On kinematic waves II. A theory of traffic flow on long crowded roads
The one-sided lipschitz condition in the follow-the-leader approximation of scalar conservation laws
On existence, stability and many-particle approximation of solutions of 1D Hughes' model with linear costs

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