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Digital archive of theses discussed at the University of Pisa

 

Thesis etd-02222019-165729


Thesis type
Tesi di dottorato di ricerca
Author
LEOCATA, MARTA
URN
etd-02222019-165729
Thesis title
Some perspectives on mathematical modeling for aggregation phenomena
Academic discipline
MAT/06
Course of study
MATEMATICA
Supervisors
tutor Prof. Flandoli, Franco
Keywords
  • Aggregation
  • Interacting diffusion system
  • Scaling limit
  • Transport diffusion equation.
  • Vlasov equation
Graduation session start date
01/03/2019
Availability
Full
Summary
The main theme of the thesis here proposed is given by the bio-physical phenomenon of aggregation. More specifically we propose some developments in the direction of scaling limits. More specifically, given some PDE (or a system of PDEs), that describe macroscopically a specific phenomena, we propose a microscopic view through a proper system of interacting particles system (in a continuous in time and space setting). In the first chapter we work on a microscopic approach to a PDE which describes cell-cell adhesion (transport-diffusion equation). In the second chapter we focus on system of particles interacting with themselves and with an incompressible fluid. In particular we work on a scaling limit for the Vlasov Fokker Planck Navier Stokes system. Finally in the third chapter we present an averaging result, applied to the study of evolution of a cancerous population, which present a peculiar type of aggregation.
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