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

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.

31 pages, 1 figure

References in corpus (2)

• A well-posedness theory in measures for some kinetic models of collective motion
• Pedestrian flows in bounded domains with obstacles

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