Tosin, Andrea; Frasca, Paolo Existence and approximation of probability measure solutions to models of collective behaviors. (English) Zbl 1262.35162 Netw. Heterog. Media 6, No. 3, 561-596 (2011). Summary: We consider first order differential models of collective behaviors of groups of agents, based on the mass conservation equation. Models are formulated taking the spatial distribution of the agents as the main unknown, expressed in terms of a probability measure evolving in time. We develop an existence and approximation theory of the solutions to such models and we show that some recently proposed models of crowd and swarm dynamics fit our theoretic paradigm. Cited in 17 Documents MSC: 35L65 Hyperbolic conservation laws 35Q70 PDEs in connection with mechanics of particles and systems of particles 35Q91 PDEs in connection with game theory, economics, social and behavioral sciences Keywords:systems of interacting agents; probability distribution; continuity equation; nonlocal flux; mass conservation equation PDFBibTeX XMLCite \textit{A. Tosin} and \textit{P. Frasca}, Netw. Heterog. Media 6, No. 3, 561--596 (2011; Zbl 1262.35162) Full Text: DOI arXiv