Nishida, Takaaki; Imai, Kazuo Global solutions to the initial value problem for the nonlinear Boltzmann equation. (English) Zbl 0344.35003 Publ. Res. Inst. Math. Sci., Kyoto Univ. 12, 229-239 (1976). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 52 Documents 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 PDFBibTeX XMLCite \textit{T. Nishida} and \textit{K. Imai}, Publ. Res. Inst. Math. Sci. 12, 229--239 (1976; Zbl 0344.35003) Full Text: DOI 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. </.). [6] Kato, T., Perturbation Theory for Linear Operators, Springer Verlag, New York, 1966. · Zbl 0148.12601 [7] McLennan, J., Convergence of the Chapman-Enskog expansion for the linearized Boltzmann equation, Phys. of Fluids, 8 (1965), 1580-1584. [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. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.