Abstract
The existence theory for the nonlinear Boltzmann equation is discussed for an infinite region in the spatially homogeneous case. We show that the solution is given by a nonlinear contraction semigroup. It is found that theH-theorem holds and that the system approaches equilibrium.
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Literatur
Povzner, A. Ya.: Zur Boltzmanngleichung in der kinetischen Theorie der Gase. Mat. Sb.58, 65–86 (1962).
Grünbaum, F. A.: Propagation of chaos for the Boltzmann equation. Arch. Rational Mech. Anal.42, 323–345 (1971).
Dorroh, J. R.: Some classes of semi-groups of nonlinear transformations and their generators. J. Math. Soc. Japan20 (3), 437–455 (1968).
Bourbaki, N.: Intégration, chapitres 1, 2, 3 et 4. Paris: Hermann 1965.
Bourbaki, N.: Intégration, chapitre 5. Paris: Hermann 1967.
Yosida, K.: Functional analysis. Berlin-Heidelberg-New York: Springer 1968.
McKean, H. P.: Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas. Arch. Rational Mech. Anal.21, 343–367 (1966).
Morgenstern, D.: Analytical studies related to the Maxwell-Boltzmann equation. J. Rational Mech. Anal.4, 533–555 (1955).
Trotter, H. F.: Approximation of semi-groups of operators. Pacific J. Math.8 (4), 887–919 (1958).
Dieudonné, J.: Foundations of modern analysis. New York: Academic Press 1960.
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Bodmer, R. Zur Boltzmanngleichung. Commun.Math. Phys. 30, 303–334 (1973). https://doi.org/10.1007/BF01645507
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DOI: https://doi.org/10.1007/BF01645507