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arxiv: 1605.05883 · v1 · pith:MDFHV7FVnew · submitted 2016-05-19 · 🧮 math.AP

Deterministic particle approximation of scalar conservation laws

Marco Di Francesco , Simone Fagioli , Massimiliano D. Rosini This is my paper
classification 🧮 math.AP
keywords conservationscalarapproximationnonlinearparticlecomplementedconditiondeterministic
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In this paper we prove that the unique entropy solution to a scalar nonlinear conservation law with strictly monotone velocity and nonnegative initial condition can be rigorously obtained as the large particle limit of a microscopic follow-the-leader type model, which is interpreted as the discrete Lagrangian approximation of the nonlinear scalar conservation law. The result is complemented with some numerical simulations.

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  1. A stiff limit of non-homogeneous conservation laws for crowd motion modeling

    math.AP 2026-05 unverdicted novelty 7.0

    A new type of PDE for selective density-constrained crowd motion is obtained as the stiff limit of conservation laws, with existence of solutions proven via uniform BV estimates and compactness.