Segregation and mixing in degenerate diffusion in population dynamics

We study the qualitative properties of degenerate diffusion equations used to describe dispersal processes in population dynamics. For systems of interacting populations, the forms of the diffusion models used determine if the population will intermix or remain disjoint (segregated). The dynamics and stability of segregation boundaries between competing populations is analyzed. General population models with segregation and mixing interactions are derived and connections to behavior in fluid mechanical systems are addressed.