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A mathematical theory is introduced in this book to unify a large class of nonlinear partial differential equation (PDE) models for better understanding and ana

Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory,

This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained

* Examines a nonlinear system of parabolic PDEs arising in mathematical biology and statistical mechanics * Describes the whole picture, i.e., the mathematical

This book discusses vortex dynamics theory from physics, mathematics, and engineering perspectives. It includes nine chapters that cover a variety of research r