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      <dc:title>Macroscopic Limits, Self-Organization and Stability in Systems with Singular Interactions Arising from Hydrodynamics and Life Sciences</dc:title>
      <dc:creator>Poyato Sánchez, Jesús David</dc:creator>
      <dc:contributor>Soler Vizcaino, Juan Segundo</dc:contributor>
      <dc:contributor>Universidad de Granada. Programa de Doctorado en Física y Matemáticas</dc:contributor>
      <dc:subject>Macroscopic Limits</dc:subject>
      <dc:subject>Self-organization</dc:subject>
      <dc:subject>Mathematical models</dc:subject>
      <dc:subject>Hydrodynamics</dc:subject>
      <dc:subject>Life Sciences</dc:subject>
      <dc:description>This dissertation is centered around the analysis of non-linear partial differential equations that&#xd;
arise from models in physics, mathematical biology, social sciences and neuroscience. Specifically,&#xd;
we address a particular family of models that have been coined in the literature with the&#xd;
name of “collective dynamics models”. The main idea is that from basic rules stating how a&#xd;
system of particles interact, the population often has the ability to self-organize collectively as&#xd;
a unique entity and it amounts to different emergent phenomena depending on the particular&#xd;
context., e.g., swarming, flocking, schooling, synchronization, etc.&#xd;
Although these models appear in completely different settings, what make them so special&#xd;
from a mathematical point of view is the fact that their structural resemblance allow us to&#xd;
tackle them with common abstract mathematical tools. Indeed many relevant improvements&#xd;
and mathematical methods have emerged from this interface as we tackle the different effects&#xd;
that we can encounter (e.g., kinetic theory, stochastic equations, mean field limits, propagation&#xd;
of chaos, hydrodynamic limits, potential theory, optimal transport, etc).</dc:description>
      <dc:date>2019-10-21T08:16:12Z</dc:date>
      <dc:date>2019-10-21T08:16:12Z</dc:date>
      <dc:date>2019</dc:date>
      <dc:date>2019-10-07</dc:date>
      <dc:type>info:eu-repo/semantics/doctoralThesis</dc:type>
      <dc:identifier>Poyato 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. [http://hdl.handle.net/10481/57445]</dc:identifier>
      <dc:identifier>9788413063324</dc:identifier>
      <dc:identifier>http://hdl.handle.net/10481/57445</dc:identifier>
      <dc:language>eng</dc:language>
      <dc:rights>http://creativecommons.org/licenses/by-nc-nd/3.0/es/</dc:rights>
      <dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
      <dc:rights>Atribución-NoComercial-SinDerivadas 3.0 España</dc:rights>
      <dc:publisher>Universidad de Granada</dc:publisher>
   </ow:Publication>
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