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This monograph is devoted to recent mathematical theories on the bottom up self-organization observed in closed and isolated thermo-dynamical systems. Its main features include:
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- New mathematical results observed in nonlinear systems significantly associated with the physical background on self-organization
- Mathematically self-contained descriptions based on systematic and comprehensive descriptions of recently developed mathematical techniques
- Fusion of many areas by strongly supported theoretical leaderships, including, chemotaxis, turbulence, fluid motion, reaction, and network
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Preface --> Contents:
- Chemotaxis:
- Keller–Segel Systems
- Blowup in Finite Time
- Scaling Limit
- Residual Vanishing
- Bounded Domains
- Simple Blowup Points
- Blowup in Infinite Time
- A Recursive Hierarchy
- Initial Mass Quantization
- Bounded Free Energy
- Notes
- 2D Turbulence:
- Point Vortices
- Mean Field Limit
- Patch Model
- Point Vortex Limit
- Kinetic Model
- Boltzmann-Poisson Equation — Classical Theory
- Geometric Structure
- sup + inf Inequality
- Radial Solutions
- Laplace-Beltrami Operators
- Mean Value Theorems
- Recursive Control of the Hamiltonian
- Convex Domains
- Notes
- Fluid Motion:
- Self-Gravitating Fluids
- Plasma Confinements
- Maximum Entropy Production
- Degenerate Parabolic Equations
- Structure of the Blowup Set
- Stationary States
- Notes
- Reaction:
- Mathematical Modeling of Reaction
- Thermodynamics of Reaction Diffusion
- Critical Dimension of Lotka-Volterra Systems
- Virus Dynamics
- Dissipative Systems with Quadratic Growth
- L 1 -Compactness of the Orbit
- Classical Solutions for 2 D Case
- Spatial Homogenization
- Notes
- Network:
- Chemical Reaction Network
- Multi-Component Reaction
- Entropy Dissipation
- Logarithmic Sobolev Inequality
- Pathway Grouping
- Nested Periodic Orbits
- Dynamical Equilibrium and Its Break Down
- Transient Oscillation
- Notes
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--> Readership: Researchers in partial differential equations, mathematical modeling, mathematical physics. -->
Nonlinear PDE;Chemotaxis;Turbulence;Fluid Motion;Reaction;Network0 Key Features:
- New mathematical results observed in nonlinear systems significantly associated with the physical background on self-organization
- Mathematically self-contained descriptions based on systematic and comprehensive descriptions of recently developed mathematical techniques
- Fusion of many areas by strongly supported theoretical leaderships, including, chemotaxis, turbulence, fluid motion, reaction, and network
