ETD

• Aggregation
• Interacting diffusion system
• Scaling limit
• Transport diffusion equation.
• Vlasov equation

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.