On Fundamental Equations of Spatially Independent Problems in Neutron Thermalization Theory

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概要

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• The linearized Boltzmann equation describing the velocity distribution of neutrons in an infinite monatomic gas is studied in the framework of the theory of Hilbert space. The corresponding eigenvalue problem is also investigated. It is found that the set of all eigenfunctions does not form a complete set. This result is contrary to the anticipation which seems to have been existed widely up to date. The more precise nature of the spectrum is examined by means of the perturbation theory of operators in Hilbert space. Especially the essential spectrum and the absolutely continuous part of the spectrum are determined completely. The asymptotic behavior of the solution of the time-dependent equation is stated as a consequence of our results on the spectrum. Proofs are mathematically rigorous and any argument of heuristic or inconclusive character is avoided. Finally a conjecture on the eigenfunction expansion formula is stated.

• 理論物理学刊行会の論文
• 1964-10-25

著者

• Shizuta Yasushi

  Department Of Applied Mathematics And Physics Faculty Of Engineering Kyoto University

• SHIZUTA Yasushi

  Department of Applied Mathematics and Physics Faculty of Engineering, Kyoto University

関連論文

• The trace theorem on anisotropic Sobolev spaces
• On the normal form of the symmetric hyperbolic-parabolic systems associated with the conservation laws
• A Note on Spatially Independent Problems of Neutron Thermalization Theory
• On Fundamental Equations of Spatially Independent Problems in Neutron Thermalization Theory
• On Cabannes' $32$-Velocity Models of the Boltzmann Equation

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