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math.AP2024
Deterministic particle method for nonlinear nonlocal scalar balance equations
Emanuela Radici, Federico Stra
We study a deterministic particle scheme to solve a scalar balance equation with nonlocal interaction and nonlinear mobility used to model congested dynamics. The main novelty with…
math.AP2024
Measure solutions, smoothing effect, and deterministic particle approximation for a conservation law with nonlocal flux
M. Di Francesco, S. Fagioli, E. Radici
We consider a class of nonlocal conservation laws with an interaction kernel supported on the negative real half-line and featuring a decreasing jump at the origin. We provide, for…
math.AP2024
On a degenerate second order traffic model: existence of discrete evolutions, deterministic many-particle limit and first order approximation
Dario Mazzoleni, Emanuela Radici, Filippo Riva
We propose and analyse a new microscopic second order Follow-the-Leader type scheme to describe traffic flows. The main novelty of this model consists in multiplying the second ord…