2 research outputs found
A Nonlinear Heat Equation Arising from Automated-Vehicle Traffic Flow Models
In this paper, a new nonlinear heat equation is studied that arises as a
model of the collective behavior of automated vehicles. The properties of the
solutions of this equation are studied by introducing the appropriate notion of
a weak solution that requires certain entropy-like conditions. To obtain an
approximation of the solution of the nonlinear heat equation, a new
conservative first-order finite difference scheme is proposed that respects the
corresponding entropy conditions, and certain links between the weak solution
and the numerical scheme are provided. Finally, a traffic simulation scenario
and a comparison with the Lighthill-Witham-Richards (LWR) model are provided,
illustrating the benefits of the use of automated vehicles.Comment: 36 pages, 9 figure