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dc.contributor.advisorSoler Vizcaino, Juan Segundo 
dc.contributor.authorPoyato Sánchez, Jesús David
dc.contributor.otherUniversidad de Granada. Programa de Doctorado en Física y Matemáticases_ES
dc.identifier.citationPoyato Sánchez, Jesús David. Macroscopic Limits, Self-Organization and Stability in Systems with Singular Interactions Arising from Hydrodynamics and Life Sciences. Granada: Universidad de Granada, 2019. []es_ES
dc.description.abstractThis dissertation is centered around the analysis of non-linear partial differential equations that arise from models in physics, mathematical biology, social sciences and neuroscience. Specifically, we address a particular family of models that have been coined in the literature with the name of “collective dynamics models”. The main idea is that from basic rules stating how a system of particles interact, the population often has the ability to self-organize collectively as a unique entity and it amounts to different emergent phenomena depending on the particular context., e.g., swarming, flocking, schooling, synchronization, etc. Although these models appear in completely different settings, what make them so special from a mathematical point of view is the fact that their structural resemblance allow us to tackle them with common abstract mathematical tools. Indeed many relevant improvements and mathematical methods have emerged from this interface as we tackle the different effects that we can encounter (e.g., kinetic theory, stochastic equations, mean field limits, propagation of chaos, hydrodynamic limits, potential theory, optimal transport, etc).es_ES
dc.description.sponsorshipTesis Univ. Granada.es_ES
dc.description.sponsorshipEsta tesis ha sido realizada con financiación del Ministerio de Educación, Cultura y Deporte, subprograma de Formación del Profesorado Universitario (FPU), referencia FPU14/06304. El doctorando ha recibido además financiación parcial de los siguientes proyectos de investigación: MTM2014-53403-R (MINECO/FEDER), RTI2018-098850-B-I00 (MICINN) y FQP-954 (Junta de Andalucía). Las estancias realizadas con objeto de obtener la mención internacional han sido financiadas por el Ministerio de Educación, Cultura y Deporte, subprograma de ayudas a la movilidad para estancias breves y traslados temporales con referencias EST16/00774 y EST17/00518.es_ES
dc.publisherUniversidad de Granadaes_ES
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.subjectMacroscopic Limitses_ES
dc.subjectMathematical models es_ES
dc.subjectHydrodynamics es_ES
dc.subjectLife Scienceses_ES
dc.titleMacroscopic Limits, Self-Organization and Stability in Systems with Singular Interactions Arising from Hydrodynamics and Life Scienceses_ES
europeana.dataProviderUniversidad de Granada. España.es_ES

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Atribución-NoComercial-SinDerivadas 3.0 España
Except where otherwise noted, this item's license is described as Atribución-NoComercial-SinDerivadas 3.0 España