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Analysis of kinetic and macroscopic models of pursuit-evasion dynamics. (English) Zbl 1354.92061

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.

MSC:

92D25 Population dynamics (general)
74A25 Molecular, statistical, and kinetic theories in solid mechanics
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