A well-posedness theory in measures for some kinetic models of collective motion
Cañizo Rincón, José Alfredo (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Carrillo de la Plata, José Antonio (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Rosado Linares, Jesús (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica

Imprint: Centre de Recerca Matemàtica 2009
Description: 26 p.
Abstract: We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the behavior of large groups of animals, such as flocks of birds, swarms, or schools of fish. Our aim is to give a well-posedness theory for general models which possibly include a variety of effects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging effect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and self-propulsion effects, which take into account effects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models.
Rights: Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús Creative Commons
Language: Anglès
Series: Centre de Recerca Matemàtica. Prepublicacions
Series: Prepublicacions del Centre de Recerca Matemàtica ; 885
Document: article ; submittedVersion
Subject: Estabilitat ; Cinemàtica ; Interacció

Adreça alternativa: https://hdl.handle.net/2072/46794

26 p, 261.3 KB

The record appears in these collections:
Research literature > Preprints

 Record created 2010-04-14, last modified 2020-11-19

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