Kinetic Transport Equations

  • Wilhelm Brenig


Transport equations in the widest sense describe the transport of physical properties (mass, momentum, energy, heat, magnetism, charge, etc.) in space. Diffusion theory and hydrodynamics use transport equations in this sense. In a more restricted sense they describe transport in phase space, i.e. (p, r)-space. We are going to use the notation in this more restricted sense. In the heading of this chapter we have indicated this by the term kinetic.


Transport Equation Boltzmann Equation Vlasov Equation Subtraction Term Collision Term 
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  1. 33.1
    Boltzmann, L.: Wien. Ber. 66, 213, 275 (1872); Lectures on Gas Theory, translated by G. Brash ( Berkeley, CA 1964 )Google Scholar
  2. 33.2
    Vlasov, A.A.: Sov. Phys. - JETP 8, 291 (1938)Google Scholar
  3. 33.3
    Sommerfeld, A.: Z. Phys. 47, 1 (1928)ADSCrossRefGoogle Scholar
  4. 33.4
    Peierls, R.: Ann. Phys. (Leipzig) 3, 1055 (1929)ADSGoogle Scholar
  5. 33.5
    Landau, LD., Khalatnikov, I.M.: Zh. Eksp. Teor. Fiz. 19, 637, 709 (1949)Google Scholar
  6. 33.6
    Landau, L.D.: Sov. Phys. - JETP 5, 101 (1957)zbMATHGoogle Scholar
  7. 33.7
    Brenig, W.: Statistische Theorie der Wärme I. Gleichgewicht, 2nd ed. ( Springer, Berlin, Heidelberg 1983 )Google Scholar
  8. 33.8
    Wigner, E.: Phys. Rev. 40, 749 (1932)ADSzbMATHCrossRefGoogle Scholar
  9. 33.9
    Bogolubov, N.N.: J. Phys. (USSR) 10, 256 (1946) [English transl. in Studies in Statistical Mechanics, Vol. 1, ed. by J. de Boer, G£. Uhlenbeck (North-Holland, Amsterdam 1962)]Google Scholar
  10. 3.10
    Kadanoff, LJP., Baym, G.: Quantum Statistical Mechanics (Benjamin, New York 1962 )zbMATHGoogle Scholar

Additional Reading

  1. Born, M., Green, H.S.: Proc. R. Soc. London A 188, 10 (1946); A 190, 455 (1947)MathSciNetADSzbMATHCrossRefGoogle Scholar
  2. Kirkwood, J.G.: J. Chem. Phys. 14, 180 (1946)ADSCrossRefGoogle Scholar
  3. Yvon, J.: Acta Sci. Ind., nos. 542, 543 (1937)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Wilhelm Brenig
    • 1
  1. 1.Physik-DepartmentTechnische Universität MünchenGarchingFed. Rep. of Germany

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