@misc{10481/57445,
year = {2019},
url = {http://hdl.handle.net/10481/57445},
abstract = {This 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).},
organization = {Tesis Univ. Granada.},
organization = {Esta 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.},
publisher = {Universidad de Granada},
keywords = {Macroscopic Limits},
keywords = {Self-organization},
keywords = {Mathematical models},
keywords = {Hydrodynamics},
keywords = {Life Sciences},
title = {Macroscopic Limits, Self-Organization and Stability in Systems with Singular Interactions Arising from Hydrodynamics and Life Sciences},
author = {Poyato Sánchez, Jesús David},
}