Journal of Statistical Physics, Vol. 55, Nos. 3/4, 1989. p. 579-600.
We consider a nonlinear reaction-diffusion model: n Brownian particles move independently in R^d 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 we characterize a wide range of speeds at which the radius goes to zero. Within this range we 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.