The authors prove existence of solutions for a model where a transported crowd rho1 and a sandpile-like, capacity-respecting crowd rho2 coexist, and demonstrate the dynamics numerically.
A granular model for crowd motion and pedestrian flow
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abstract
We study a granular model for congested crowd motion and pedestrian flow. Our approach is based on an approximation through a Hele-Shaw type equation involving a degenerate operator of $p$-Laplacian type and a linear drift, for which we prove existence and uniqueness using nonlinear semigroup methods and the doubling variables technique. Our main result shows that, as $p \to \infty$, the weak solutions of the $p-$problem converge to a variational solution of the congested crowd motion problem.
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Congested Crossing Pedestrian Traffic Flow : Dispersion vs. Transport in Crowded Areas
The authors prove existence of solutions for a model where a transported crowd rho1 and a sandpile-like, capacity-respecting crowd rho2 coexist, and demonstrate the dynamics numerically.