Existence and uniqueness of weak entropy solutions for nonlocal nonlinear scalar conservation laws is proven on short time horizons via fixed-point methods, extending to any finite horizon under additional assumptions.
On the modeling of traffic and crowds: A survey of models, speculations, and perspectives
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Presents a coupled prediction-correction variant of Hughes' crowd model and uses numerical simulations to suggest progress toward its well-posedness.
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Existence and uniqueness of nonlocal nonlinear conservation laws via fixed-point methods
Existence and uniqueness of weak entropy solutions for nonlocal nonlinear scalar conservation laws is proven on short time horizons via fixed-point methods, extending to any finite horizon under additional assumptions.
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A coupled prediction-correction Hughes' model for congested crowd motion
Presents a coupled prediction-correction variant of Hughes' crowd model and uses numerical simulations to suggest progress toward its well-posedness.