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In this paper we consider first order differential models of collectivebehaviors of groups of agents based on the mass conservation equation. Modelsare formulated taking the spatial distribution of the agents as the mainunknown, expressed in terms of a probability measure evolving in time. Wedevelop an existence and approximation theory of the solutions to such modelsand we show that some recently proposed models of crowd and swarm dynamics fitour theoretic paradigm.

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