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On the Boltzmann equation. I: Existence. (English) Zbl 0245.76059


MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
45J05 Integro-ordinary differential equations
47J05 Equations involving nonlinear operators (general)
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[1] Arkeryd, L., On the Boltzmann equation, Part II. The full initial-value problem, following in this issue. · Zbl 0245.76060
[2] Arkeryd, L., An existence theorem for the Boltzmann equation. (1971), to appear.
[3] Carleman, T., Théorie cinétique des gaz. Uppsala 1957.
[4] Edwards, R. E., Functional Analysis. N.Y. 1965 (see p. 274 and p. 549).
[5] Grad, H., Asymptotic equivalence of the Navier-Stokes and nonlinear Boltzmann equation. Proc. of Symp. in Appl. Math. 17, 154–183 (1965). · Zbl 0144.48203 · doi:10.1090/psapm/017/0184507
[6] McShane, E. J., Integration. Princeton 1947 (see p. 176).
[7] 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. U.S.A. 40, 719–721 (1954). · Zbl 0056.20506 · doi:10.1073/pnas.40.8.719
[8] Morgenstern, D., Analytical studies related to the Maxwell-Boltzmann equation. J. Rational Mech. Anal. 4, 533–555 (1955). · Zbl 0068.31505
[9] Povzner, A. Ja., About the Boltzmann equation in kinetic gas theory. Mat. Sborn. 58 (100), 65–86 (1962).
[10] Wild, E., On Boltzmann’s equation in the kinetic theory of gases. Proc. Cambr. Phil. Soc. 47, 602–609 (1951). · Zbl 0043.43703 · doi:10.1017/S0305004100026992
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