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arXiv · 2611.04503

Balance laws with measure valued source for commuting dynamics

Fabio Ancona·Annalisa Cesaroni·Elio Marconi
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Abstract

In this paper we consider balance laws with measure-valued sources modeling commuters traveling along a road from residential to workplace locations. We introduce a notion of $(m_I, m_F)$-entropy solution, prove a compactness result for this class, and establish existence of solutions with prescribed spatial marginals for the sources representing the lodging and workplace distributions. Moreover, adopting a Lagrangian viewpoint, we describe commuting strategies as measures on Lipschitz curves with assigned entry and exit times, compatible with a given transport plan. Using the compactness result and a semi-discrete micro-macro scheme with source, based on the celebrated Follow-the-Leader model, we prove existence of admissible commuting strategies. Finally we prove the existence of optimal solutions for classical traffic cost functionals.

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Fabio Ancona, Annalisa Cesaroni, Elio Marconi. 2026-11-03. Balance laws with measure valued source for commuting dynamics. https://arxiv.org/abs/2611.04503

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