Macroscopic Limits, Self-Organization and Stability in Systems with Singular Interactions Arising from Hydrodynamics and Life Sciences
Poyato Sánchez, Jesús David
Soler Vizcaino, Juan Segundo
Universidad de Granada. Programa de Doctorado en Física y Matemáticas
Macroscopic Limits
Self-organization
Mathematical models
Hydrodynamics
Life Sciences
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).
2019-10-21T08:16:12Z
2019-10-21T08:16:12Z
2019
2019-10-07
info:eu-repo/semantics/doctoralThesis
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]
9788413063324
http://hdl.handle.net/10481/57445
eng
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/openAccess
Atribución-NoComercial-SinDerivadas 3.0 España
Universidad de Granada