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Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas

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Bibliography

  1. Carleman, T., Problèmes Mathématiques dans la théorie cinétique des gaz. Uppsala 1957.

  2. Dresden, M., Scientific Theory Applied to Hydrodynamics. Dallas: Magnolia Petroleum Company 1956.

    Google Scholar 

  3. Ford, G. W., & G. E. Uhlenbeck, Lectures in Statistical Mechanics. Providence 1963.

  4. Kac, M., Probability and Related Topics in the Physical Sciences. New York 1959.

  5. Linnik, Yu.V., An information-theoretic proof of the central limit theorem with the Lindeberg condition. Teor. Veroyatnost. i ee Primenen. 4, 288–299 (1959).

    Google Scholar 

  6. McKean, H.P., Jr., Entropy is the only increasing functional of Kac's 1-dimensional caricature of a Maxwellian gas. Z. für Wahrscheinlichkeitstheorie 2, 167–172 (1963).

    Google Scholar 

  7. Maxwell, J.C., Scientific Papers (2). New York 1952.

  8. Morgenstern, D., General existence and uniqueness proof for spatially homogeneous solutions of the Maxwell-Boltzmann equation in the case of Maxwellian molecules. Proc. Nat. Acad. Sci. USA 40, 719–721 (1954).

    Google Scholar 

  9. Povzner, A.Ya., On Boltzmann's equation in the kinetic theory of gases. Mat. Sb. 58, 63–86 (1962).

    Google Scholar 

  10. Trotter, H., An elementary proof of the central limit theorem. Arch. Math. 10, 226–234 (1959).

    Google Scholar 

  11. Wild, E., On Boltzmann's equation in the kinetic theory of gases. Proc. Camb. Phil. Soc. 47, 602–609 (1951).

    Google Scholar 

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Communicated by M. Kac

The partial support of the Office of Naval Research and of the National Science Foundation, NSF G-19684, is gratefully acknowledged.

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McKean, H.P. Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas. Arch. Rational Mech. Anal. 21, 343–367 (1966). https://doi.org/10.1007/BF00264463

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