scholarly journals Mean-field limit versus small-noise limit for some interacting particle systems

2016 ◽  
Vol 10 (1) ◽  
Author(s):  
Samuel Herrmann ◽  
Julian Tugaut
Keyword(s):  
Interacting Particle Systems ◽  
Mean Field ◽  
Particle Systems ◽  
Field Limit ◽  
Mean Field Limit ◽  
Small Noise ◽  
Interacting Particle ◽  
Noise Limit

scholarly journals Instantaneous control of interacting particle systems in the mean-field limit

2020 ◽  
Vol 405 ◽  
pp. 109181 ◽  
Author(s):  
Martin Burger ◽  
René Pinnau ◽  
Claudia Totzeck ◽  
Oliver Tse ◽  
Andreas Roth
Keyword(s):  
Interacting Particle Systems ◽  
Mean Field ◽  
Particle Systems ◽  
Field Limit ◽  
Mean Field Limit ◽  
Interacting Particle ◽  
The Mean ◽  
Instantaneous Control

scholarly journals The Microscopic Derivation and Well-Posedness of the Stochastic Keller–Segel Equation

2020 ◽  
Vol 31 (1) ◽  
Author(s):  
Hui Huang ◽  
Jinniao Qiu
Keyword(s):  
Existence Of Solutions ◽  
Particle System ◽  
Mean Field ◽  
Field Limit ◽  
Mean Field Limit ◽  
Unique Existence ◽  
Interacting Particle ◽  
Microscopic Derivation ◽  
The Mean ◽  
Limit Result

AbstractIn this paper, we propose and study a stochastic aggregation–diffusion equation of the Keller–Segel (KS) type for modeling the chemotaxis in dimensions $$d=2,3$$ d = 2 , 3 . Unlike the classical deterministic KS system, which only allows for idiosyncratic noises, the stochastic KS equation is derived from an interacting particle system subject to both idiosyncratic and common noises. Both the unique existence of solutions to the stochastic KS equation and the mean-field limit result are addressed.

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

2021 ◽  
Vol 31 (6) ◽  
Author(s):  
Li Chen ◽  
Esther S. Daus ◽  
Alexandra Holzinger ◽  
Ansgar Jüngel
Keyword(s):  
Interacting Particle Systems ◽  
Mean Field ◽  
Strong Solutions ◽  
Particle Systems ◽  
Mean Field Limit ◽  
Diffusion Term ◽  
Small Initial Data ◽  
Dirac Delta ◽  
Cross Diffusion ◽  
Diffusion Systems

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

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