BIRS Workshop Lecture Videos

Banff International Research Station Logo

BIRS Workshop Lecture Videos

First-order aggregation models and zero inertia limits Fetecau, Razvan


We consider a first-order aggregation model in both discrete and continuum formulations and show how it can be obtained as zero inertia limits of second-order models. The limiting procedure becomes particularly important when one considers anisotropy in the first-order discrete model, as in that case the model becomes {\em implicit}, and issues such as non-uniqueness and jump discontinuities are being brought up. To extend solutions beyond breakdown we propose a relaxation system containing a small parameter \(\epsilon\), which can be interpreted as a small amount of inertia or response time. We show that the limit \(\epsilon \to 0\) can be used as a jump criterion to select the physically correct velocities. In the continuum setting, the procedure consists in a macroscopic limit, enabling the passage from a kinetic model for aggregation to an evolution equation for the macroscopic density. This is joint work with Joep Evers, Lenya Ryzhik and Weiran Sun.

Item Media

Item Citations and Data


Attribution-NonCommercial-NoDerivatives 4.0 International