# American Institute of Mathematical Sciences

September  2011, 6(3): 561-596. doi: 10.3934/nhm.2011.6.561

## Existence and approximation of probability measure solutions to models of collective behaviors

 1 Department of Mathematics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Received  December 2010 Revised  February 2011 Published  August 2011

In this paper 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.
Citation: Andrea Tosin, Paolo Frasca. Existence and approximation of probability measure solutions to models of collective behaviors. Networks & Heterogeneous Media, 2011, 6 (3) : 561-596. doi: 10.3934/nhm.2011.6.561
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