Young Researchers Workshop:
Kinetic and macroscopic models for complex systems

Understanding the Effects of Location on Segregation: A PDE approach

Nancy Rodriguez

Stanford University

In this talk I explore the consequences that individual's desire to be with people sharing some characteristic (which we refer to as influence) and attraction to good locations has on segregation by introducing a particle-interaction model where the interaction between individuals is governed by the two effects mentioned. Since the time evolution of the particle-interaction model is governed by a large system of ordinary differential equations I will derive a family of local and non-local partial differential equations which govern the density of the population for each influence level in order to make any analysis tractable. For the remaining of the talk I will discuss a simplified case where there are two groups of individuals: one highly influential and one with no influence. The system of PDEs in this case is reminiscent of a chemotaxis model with two densities which are simultaneously advected by a given velocity field and repulsed by each other. By analyzing this system I will show that the desire to be situated in a good location enhances segregation. In fact, I will prove the existence of a unique ground state that shows that segregates the two populations.