Dynamics of Many-Particle Systems and Mean-field Equations
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Organizer(s): |
Name:
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Affiliation:
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Country:
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Hui Huang
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Hunan University
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Peoples Rep of China
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Hicham Kouhkouh
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University of Graz
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Austria
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Introduction:
| | Many-particle systems and mean-field equations are nonlocal models that play a central role in describing complex interactions across physical, biological and social systems. In many settings, large ensembles of interacting agents can be effectively described by continuum equations derived through mean-field limits. This transition from discrete particle dynamics to nonlocal partial differential equations presents deep mathematical challenges, involving singular interactions, stochastic effects, and high-dimensional behavior. Recent progress has shed new light on the rigorous derivation of mean-field models, the qualitative properties of nonlocal PDEs, and the development of structure-preserving numerical methods. At the same time, emerging tools from optimal transport, variational analysis, and scientific machine learning offer new perspectives on classical problems, such as pattern formation, stability, and long-time asymptotics. This special session will bring together researchers working at the interface of many-particle dynamics, nonlocal models, and continuum limits, aiming to foster a deeper understanding of the analytical, probabilistic, and computational aspects of these systems.
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