Communications in Mathematical Sciences

Volume 14 (2016)

Number 8

Analysis of kinetic and macroscopic models of pursuit-evasion dynamics

Pages: 2253 – 2286

DOI: https://dx.doi.org/10.4310/CMS.2016.v14.n8.a7

Authors

Thierry Goudon (Inria, Sophia Antipolis Méditerranée Research Centre, Project COFFEE, and Université Nice Sophia Antipolis, Nice, France)

Luis Urrutia (Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, Spain)

Abstract

We analyse kinetic and macroscopic models intended to describe pursuit-evasion dynamics. We investigate well-posedness issues and the connection between the two model, based on asymptotic analysis. In particular, in dimension $2$, we show that the macroscopic system has some regularizing effects: bounded solutions are produced, even when starting from integrable but possibly unbounded data. Our proof is based on De Giorgi’s method.

Keywords

collective behaviour, self-propelling particles, self-organization, kinetic models, hydrodynamic models, regularity of solutions, De Giorgi’s method

2010 Mathematics Subject Classification

74A25, 76N10, 92C17, 92D25

Published 26 October 2016