Rigorous Derivation of Population Cross-Diffusion Systems from Moderately Interacting Particle Systems

Abstract Population cross-diffusion systems of Shigesada–Kawasaki–Teramoto type are derived in a mean-field-type limit from stochastic, moderately interacting many-particle for multiple population species the whole space. The diffusion term stochastic model depends nonlinearly on interactions between individuals, and drift is gradient environmental potential. In first step, mean-field leads to an intermediate nonlocal model. local system second step moderate scaling regime, when interaction potentials approach Dirac delta distribution. global existence strong solutions proved sufficiently small initial data. Furthermore, numerical simulations particle level presented.