Chemotaxis, Reaction, Network

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-organizationMathematically self-contained descriptions based on systematic and comprehensive descriptions of recently developed mathematical techniquesFusion of many areas by strongly supported theoretical leaderships, including, chemotaxis, turbulence, fluid motion, reaction, and networkSample Chapter(s)
Preface

Contents:Chemotaxis:Keller–Segel SystemsBlowup in Finite TimeScaling LimitResidual VanishingBounded DomainsSimple Blowup PointsBlowup in Infinite TimeA Recursive HierarchyInitial Mass QuantizationBounded Free Energy Notes2D Turbulence:Point VorticesMean Field LimitPatch ModelPoint Vortex LimitKinetic ModelBoltzmann-Poisson Equation — Classical TheoryGeometric Structuresup + inf InequalityRadial SolutionsLaplace-Beltrami OperatorsMean Value TheoremsRecursive Control of the HamiltonianConvex Domains NotesFluid Motion:Self-Gravitating FluidsPlasma ConfinementsMaximum Entropy ProductionDegenerate Parabolic EquationsStructure of the Blowup SetStationary States NotesReaction:Mathematical Modeling of ReactionThermodynamics of Reaction DiffusionCritical Dimension of Lotka-Volterra SystemsVirus DynamicsDissipative Systems with Quadratic GrowthL1-Compactness of the OrbitClassical Solutions for 2D CaseSpatial Homogenization NotesNetwork:Chemical Reaction NetworkMulti-Component ReactionEntropy DissipationLogarithmic Sobolev InequalityPathway GroupingNested Periodic OrbitsDynamical Equilibrium and Its Break DownTransient Oscillation Notes
Readership: Researchers in partial differential equations, mathematical modeling, mathematical physics.
Nonlinear PDE;Chemotaxis;Turbulence;Fluid Motion;Reaction;Network0Key Features:New mathematical results observed in nonlinear systems significantly associated with the physical background on self-organizationMathematically self-contained descriptions based on systematic and comprehensive descriptions of recently developed mathematical techniquesFusion of many areas by strongly supported theoretical leaderships, including, chemotaxis, turbulence, fluid motion, reaction, and network