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On the non-linear Boltzmann equation in unbounded domains

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References

  1. N. Bellomo & G. Toscani “On the Cauchy problem for the nonlinear Boltzmann Equation: global existence, uniqueness and asymptotic stability”. J. Math. Phys. 26, 1985, 334–338.

    Google Scholar 

  2. N. Bellomo, R. Illner & G. Toscani, “Sur le problème de Cauchy pour l'équation de Boltzmann semidiscrète”. C.R.A.S. 299, 1984, 835–838.

    Google Scholar 

  3. R. Caflish, “Boltzmann Equation with soft potential: Part I, Linear spatially homogeneous”. Commun. Math. Phys. 74, 1980, 71–95.

    Google Scholar 

  4. T. Carleman, “Problèmes mathématiques dans la théorie cinétique des gaz”. Almquist & Wiksell, Uppsala 1957.

    Google Scholar 

  5. C. Cercignani, “Theory and application of the Boltzmann Equation”. Scottish Academic Press, Edinburgh 1975.

    Google Scholar 

  6. W. Fiszdom, H. Lachowicz & A. Palchewski, “Existence problems of the nonlinear Boltzmann Equation” in Trends and Applications of Pure Mathematics to Mechanics, Lect. Note in Phys. n. 195, 1984, 63–95.

  7. H. Grad, “Principles of the kinetic theory of gases” in Handbuch der Physik, S. Flügge eds. Vol. 12, Springer-Verlag, Berlin-Göttingen-Heidelberg (1958) 205–294.

    Google Scholar 

  8. H. Grad, “Theory of rarefied gases” in Rarefied Gas Dynamics, Pergamon Press, London, 1960, 100–138.

    Google Scholar 

  9. W. Greenberg, J. Palewczak & P. F. Zweifel, “Global existence proofs for the Boltzmann Equation” in Nonequilibrium Phenomena I, The Boltzmann Equation. J. L. Lebowitz & E. W. Montroll Eds., North Holland Publishing Company, 1983, 21–49.

  10. J. P. Guiraud, “An H-theorem for a gas of rigid spheres in a bounded domain”, Colloques Internationaux du C.N.R.S. n. 236, 1974, 29–58.

  11. K. Hamdache, “Existence in the large and asymptotic behaviour for the Boltzmann Equation”. Japan J. of Appl. Math. 2, 1984.

  12. S. Kaniel & M. Shinbrot, “The Boltzmann Equation I: Uniqueness and global existence”. Commun. Math. Phys. 58, 1978, 65–84.

    Google Scholar 

  13. R. Illner & M. Shinbrot, “Global existence for a rare gas in an infinite vacuum”. Commun. Math. Phys. 95, 1984, 117–126.

    Google Scholar 

  14. T. Nishida & K. Imai, “Global solutions to the initial value problem for the nonlinear Boltzmann Equation”. Publ. Res. Inst. Math. Sci. Kyoto Univ. 12, 1977, 229–239.

    Google Scholar 

  15. Y. Shizuta & R. Asano, “Global solutions of the Boltzmann Equation in a bounded convex domain”. Proc. Japan. Acad. Ser. A Math. Sci. 53, 1977, 3–5.

    Google Scholar 

  16. L. Tartar, “Some existence theorems for semilinear hyperbolic systems in one space variable”. Univ. of Wisconsin-Madison 1980.

  17. G. Toscani & N. Bellomo, “Global existence, uniqueness and stability of the nonlinear Boltzmann Equation with almost general gas-particle interaction potential”. Proceedings of Centenario del Circolo Matematico di Palermo, Palermo 1984.

  18. G. Toscani, “Global existence and asymptotic behaviour for the discrete velocity models of the Boltzmann equation” to appear in J. Math. Phys. 1985.

  19. C. Truesdell & R. G. Muncaster, “Fundamentals of Maxwell's kinetic theory of a simple monatomic gas”. Academic Press, New York 1980.

    Google Scholar 

  20. S. Ukay, “On the existence of global solutions of mixed problems for the non-linear Boltzmann Equation”. Proc. Japan. Acad. Ser. A Math. Sci. 50, 1974, 179–184.

    Google Scholar 

  21. T. Gustafsson, private communication.

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Communicated by L. Arkeryd

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Toscani, G. On the non-linear Boltzmann equation in unbounded domains. Arch. Rational Mech. Anal. 95, 37–49 (1986). https://doi.org/10.1007/BF00280788

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