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:
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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