Young Researchers Workshop:
Multiscale phenomena: modeling, analysis and computation

Macroscopic limits and asymptotic behavior of some kinetic models in astrophysics and biology

Juan Calvo

Universitat Pompeu Fabra
[SLIDES]

The first part of the talk is devoted to discuss several macroscopic limits of certain kinetic models. These models arise for instance in some branches of Astrophysics. Specifically, we start by introducing the relativistic BGK model as a model equation for the relativistic Boltzmann equation and discussing some of its asymptotic regimes then. We deal with macroscopic limits of Fokker-Planck type models under non-standard scaling relations afterwards. In the second part of the talk we present a two species model for particles (typically molecules or cells) and study its large time asymptotics. Particles can be in one of two states: A “free” state where they move with a given velocity or an aggregated state where they do not move anymore. We show that depending only on the strength of the interaction between particles, either all of them eventually coagulate or some may escape.