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Networks and Heterogeneous Media (NHM)
 

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

Pages: 561 - 596, Volume 6, Issue 3, September 2011

doi:10.3934/nhm.2011.6.561       Abstract        References        Full Text (597.7K)       Related Articles

Andrea Tosin - Department of Mathematics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy (email)
Paolo Frasca - Department of Mathematics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy (email)

Abstract: 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.

Keywords:  Systems of interacting agents, probability distribution, continuity equation, nonlocal flux.
Mathematics Subject Classification:  Primary: 35L65, 35Q70; Secondary: 35Q91.

Received: December 2010;      Revised: February 2011;      Published: August 2011.

 References