Non Local Conservation Laws in Bounded Domains

TL;DR

This paper establishes well-posedness and stability for non-local conservation laws in bounded domains, motivated by crowd dynamics, and demonstrates the model's qualitative effectiveness through numerical simulations.

Contribution

It introduces a novel non-local operator suited for bounded domains and proves well-posedness and stability results for the associated conservation laws.

Findings

The model produces qualitatively reasonable solutions in simulations.

Stability estimates are derived for the non-local conservation laws.

The framework is motivated by and applicable to crowd dynamics modeling.

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.