Goudon, Thierry; Urrutia, Luis Analysis of kinetic and macroscopic models of pursuit-evasion dynamics. (English) Zbl 1354.92061 Commun. Math. Sci. 14, No. 8, 2253-2286 (2016). Summary: 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. Cited in 13 Documents MSC: 92D25 Population dynamics (general) 74A25 Molecular, statistical, and kinetic theories in solid mechanics Keywords:collective behaviour; self-propelling particles; self-organization; kinetic models; hydrodynamic models; regularity of solutions; De Giorgi’s method PDFBibTeX XMLCite \textit{T. Goudon} and \textit{L. Urrutia}, Commun. Math. Sci. 14, No. 8, 2253--2286 (2016; Zbl 1354.92061) Full Text: DOI