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The Boltzmann equation with a soft potential. I: Linear, spatially- homogeneous. (English) Zbl 0434.76065

76P05Rarefied gas flows, Boltzmann equation
[1]Arkeryd, L.: On the Boltzmann equation. I, II. Arch. Ration. Mech. Anal.45, 1-16 and 17-34 (1972)
[2]Chapman, S., Cowling, T.G.: The mathematical theory of non-uniform gases, 3rd ed. Cambridge: Cambridge University Press 1970
[3]Glikson, A.: On the existence of general solutions of the initial-value problem for the nonlinear Boltzmann equation with a cut-off. Arch. Ration. Mech. Anal.45, 35-46 (1972) · doi:10.1007/BF00253394
[4]Grad, H.: Principles of the kinetic theory of gases. In: Handbuch der PhysikXII, 205-294 (1958)
[5]Grad, H.: Asymptotic theory of the Boltzmann equation. II. In: Rarefied gas dynamics, 3rd Symposium, 26-59. Paris: 1962
[6]Grad, H.: Asumptotic converges of the Navier-Stokes and the nonlinear Boltzmann equations. Proc. Symp. App. Math.17, 154-183 (1965)
[7]Hirschfelder, J., Curtiss, C., Bird, R.: Molecular theory of gases and liquids. London: Wiley 1954
[8]Kaniel, S., Shinbrot, M.: The Boltzmann equation. Commun. Math. Phys.58, 65-84 (1978) · Zbl 0371.76061 · doi:10.1007/BF01624788
[9]Lanford, O.E.: Time evolution of large classical systems. In: Dynamical systems, theory, and applications. Lecture Notes in Phys.38, 1-111 (1975) · Zbl 0329.70011 · doi:10.1007/3-540-07171-7_1
[10]Maxwell, J.: On the dynamical theory of gases. In: The scientific papers of James Clark Maxwell. Cambridge: Cambridge University Press 1890
[11]Nishida, T., Imai, L.: Global solutions to the initial value problem for the nonlinear Boltzmann equation. Publ. RIMS Kyoto.12, 229-239 (1976) · Zbl 0344.35003 · doi:10.2977/prims/1195190965
[12]Schecter, M.: On the essential spectrum of an arbitrary operator. J. Math. Anal. Appl.13, 205-215 (1966) · Zbl 0147.12101 · doi:10.1016/0022-247X(66)90085-0
[13]Ukai, S.: On the existence of global solutions of mixed problem for nonlinear Boltzmann equation. Proc. Jpn. Acad.50, 179-184 (1974) · Zbl 0312.35061 · doi:10.3792/pja/1195519027