Limite hydrodynamique et hydrostatique d'un processus de contact généralisé avec réservoirs lents (Sonia Velasco, Université Paris Descartes)

We consider an interacting particle system which models the
sterile insect technique on a finite cylinder. When in contact with slow
reservoirs , the hydrodynamic limit of the latter system is a set of
coupled reaction diffusion equations with mixed boundary conditions,
boundary conditions which depends on the slow-down rates of the
reservoirs. The goal of this talk is to prove the existence of a
hydrostatic limit for a class of parameters. In other words, starting
from a microscopic equilibrium, the system will evolve  and converge to
a macroscopic equilibrium, corresponding to the unique stationary
solution of the hydrodynamic equation.