First-order aggregation models and zero inertia limits

TL;DR

This paper rigorously derives first-order aggregation models as zero inertia limits of second-order models, using measure solutions, mass transportation, and characteristic methods to connect kinetic and macroscopic descriptions.

Contribution

It provides a rigorous mathematical framework for deriving first-order aggregation models from second-order models via zero inertia limits, including both discrete and continuum cases.

Findings

Established zero inertia limit from second-order to first-order models.

Developed a measure solutions framework for aggregation models.

Applied mass transportation and characteristic methods in the analysis.

Abstract

We consider a first-order aggregation model in both discrete and continuum formulations and show rigorously how it can be obtained as zero inertia limits of second-order models. In the continuum case the procedure consists in a macroscopic limit, enabling the passage from a kinetic model for aggregation to an evolution equation for the macroscopic density. We work within the general space of measure solutions and use mass transportation ideas and the characteristic method as essential tools in the analysis.