Non Local Conservation Laws in Bounded Domains

2017/11/14 by Elena Rossi, Rossi, Elena, Rinaldo M. Colombo +1 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1711.05083

openalex publication_date 2017/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The well posedness for a class of non local systems of conservation laws in a bounded domain is proved and various stability estimates are provided. This construction is motivated by the modelling of crowd dynamics, which also leads to define a non local operator adapted to the presence of a boundary. Numerical integrations show that the resulting model provides qualitatively reasonable solutions.

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• Nonlocal conservation laws with p-norm, the singular limit problem and applications to traffic flow

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