Differential Equations

Download e-book for kindle: MEAN FIELD THEORIES AND DUAL VARIATION: A Mathematical by Takashi Suzuki

By Takashi Suzuki

A mathematical conception is brought during this booklet to unify a wide classification of nonlinear partial differential equation (PDE) versions for larger realizing and research of the actual and organic phenomena they signify. The so-called suggest box approximation strategy is followed to explain the macroscopic phenomena from definite microscopic ideas for this unified mathematical formula. key parts for this process are the notions of “duality” in response to the PDE vulnerable ideas and “hierarchy” for revealing the main points of the differently hidden secrets and techniques, akin to actual secret hidden among particle density and box focus, quantized blow up organic mechanism sealed in chemotaxis platforms, in addition to multi-scale mathematical reasons of the Smoluchowski–Poisson version in non-equilibrium thermodynamics, two-dimensional turbulence thought, self-dual gauge concept, etc. This publication exhibits how and why many alternative nonlinear difficulties are inter-connected when it comes to the homes of duality and scaling, and how to research them mathematically.

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MEAN FIELD THEORIES AND DUAL VARIATION: A Mathematical Profile Emerged in the Nonlinear Hierarchy: 2 (Atlantis Studies in Mathematics for Engineering and Science) by Takashi Suzuki


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