Abstract
We consider a nonlinear reaction-diffusion model:n Brownian particles move independently inR dand 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.
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Nappo, G., Orlandi, E. & Rost, H. A reaction-diffusion model for moderately interacting particles. J Stat Phys 55, 579–600 (1989). https://doi.org/10.1007/BF01041598
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DOI: https://doi.org/10.1007/BF01041598