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

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

2010-12-10

arxiv.org/abs/1012.2395v1

Netw. Heterog. Media, 6(3):561-596, 2011

Mathematics

Analysis of PDEs

31 pages, 1 figure

Scientific paper

10.3934/nhm.2011.6.561

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.

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