Communications in Mathematical Sciences
Volume 14 (2016)
Analysis of kinetic and macroscopic models of pursuit-evasion dynamics
Pages: 2253 – 2286
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.
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