<?xml version="1.0" encoding="UTF-8"?><?xml-stylesheet type="text/xsl" href="static/style.xsl"?><OAI-PMH xmlns="http://www.openarchives.org/OAI/2.0/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/ http://www.openarchives.org/OAI/2.0/OAI-PMH.xsd"><responseDate>2026-04-14T07:31:35Z</responseDate><request verb="GetRecord" identifier="oai:www.recercat.cat:2072/452663" metadataPrefix="oai_dc">https://recercat.cat/oai/request</request><GetRecord><record><header><identifier>oai:recercat.cat:2072/452663</identifier><datestamp>2024-06-06T09:47:04Z</datestamp><setSpec>com_2072_98</setSpec><setSpec>col_2072_378195</setSpec></header><metadata><oai_dc:dc xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:doc="http://www.lyncode.com/xoai" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
   <dc:title>A well-posedness theory in measures for some kinetic models of collective motion</dc:title>
   <dc:creator>Cañizo Rincón, José Alfredo</dc:creator>
   <dc:creator>Carrillo de la Plata, José Antonio</dc:creator>
   <dc:creator>Rosado Linares, Jesús</dc:creator>
   <dc:creator>Centre de Recerca Matemàtica</dc:creator>
   <dc:subject>Estabilitat</dc:subject>
   <dc:subject>Cinemàtica</dc:subject>
   <dc:subject>Interacció</dc:subject>
   <dc:description>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.</dc:description>
   <dc:date>2009</dc:date>
   <dc:type>Article</dc:type>
   <dc:type>Prepublicació</dc:type>
   <dc:identifier>https://ddd.uab.cat/record/54905</dc:identifier>
   <dc:identifier>urn:oai:ddd.uab.cat:54905</dc:identifier>
   <dc:language>eng</dc:language>
   <dc:relation>Centre de Recerca Matemàtica. Prepublicacions ;</dc:relation>
   <dc:rights>open access</dc:rights>
   <dc:rights>Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.</dc:rights>
   <dc:rights>https://creativecommons.org/licenses/by-nc-nd/2.5/</dc:rights>
   <dc:format>application/pdf</dc:format>
   <dc:publisher>Centre de Recerca Matemàtica</dc:publisher>
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