A reaction-diffusion model for moderately interacting particles

The authors consider a nonlinear reaction-diffusion model: n Brownian particles move independently in Rd and eventually die. The interaction, of binary type, affects only the death rate. The radius of interaction goes to zero as the number of particles increases and they characterize a wide range of speeds at which the radius goes to zero. Within this range they show a law of large numbers for the empirical distributions of the alive particles. The limit is independent of the choice of the speed and it is characterized as the solution of a nonlinear reaction-diffusion equation