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基本説明
Provides a comprehensive review of both equations and presents classical and modern applications.
Full Description
Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in 1938 and serves as a basis of plasma physics and describes large-scale processes and galaxies in astronomy, star wind theory. This book provides a comprehensive review of both equations and presents both classical and modern applications. In addition, it discusses several open problems of great importance.
Contents
Principal Concepts of Kinetic EquationsLagrangian CoordinatesVlasov-Maxwell and Vlasov-Einstein EquationsEnergetic SubstitutionIntroduction in Mathematical Theory of Kinetic EquationsOn the Family of the Steady-State Solutions of Vlasov-Maxwell SystemBoundary Value Problems for the Vlasov-Maxwell SystemBifurcation of Stationary Solutions of the Vlasov-Maxwell SystemBoltzmann EquationDiscrete Models of Boltzmann EquationMethod of Spherical Harmonics and Relaxation of Maxwellian GasDiscrete Boltzmann equation Models for MixturesQuantum Hamiltonians and Kinetic EquationsModelling of the Limit Problem for the Magnetically Noninsulated DiodeGeneralized Liouville Equation and Approximate Orthogonal Decomposition Methods
