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Global solutions to the initial value problem for the nonlinear Boltzmann equation. (English) Zbl 0344.35003


MSC:

35B45 A priori estimates in context of PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
35G20 Nonlinear higher-order PDEs
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References:

[1] Ellis, R. and Pinsky, M., The first and second fluid approximations to the linearized Boltzman equation, J. Math. Pures AppL, 54 (1975), 125-156. · Zbl 0286.35062
[2] Grad, H., Asymptotic theory of the Boltzmann equation, II, Rarefied Gas Dynamics, J. A. Laurmann, ed. Vol. I, Academic Press, New York, 1963. · Zbl 0115.45006 · doi:10.1063/1.1706716
[3] , Asymptotic equivalence of the Navier-Stokes and nonlinear Boltzmann equations, Proc. Symp. in AppL Math., Amer. Math. Soc., 17 (1965), 154-183. · Zbl 0144.48203
[4] 1 Solutions of the Boltzmann equation in an unbounded domain, Comm. Pure AppL Math., 18 (1965), 345-354. · Zbl 0138.34703 · doi:10.1002/cpa.3160180126
[5] Inoue, K. and Nishida, T., On the Broadwell model of the Boltzmann equation for a simple discrete velocity gas, to appear in AppL Math, and Optimization (Intern. </.).
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[8] Nicolaenco, B., Dispersion laws for plane wave propagation and the Boltzmann equation, Seminar on the Boltzmann Equation, Courant Inst. Math. Sci., NYU, F. Grunbaum, ed. (1972).
[9] Scharf, G., Functional-analytic discussion of the linearized Boltzmann equation, Helv. Phys. Acta, 40 (1967), 929-945. · Zbl 0154.46405
[10] -, Normal solutions of the linearized Boltzmann equation, Helv. Phys. Acta, 42 (1969), 5-22. · Zbl 0219.76087
[11] Schechter, M., On the essential spectrum of an arbitrary operator I, J. Math. Anal. AppL, 13 (1966), 205-215. · Zbl 0147.12101 · doi:10.1016/0022-247X(66)90085-0
[12] Ukai, S., On the existence of global solutions of mixed problem for nonlinear Boltzmann equation, Proc. Japan Acad., 50 (1974), 179-184. · Zbl 0312.35061 · doi:10.3792/pja/1195519027
[13] Arseniev, A., The Cauchy problem for the linearized Boltzman equation, J. Comput. Math, and Math. Phps. (USSR), 5 (1965), 864-882.
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