Geodesic
Neutron transport initial value problem in non-multiplying medium
Applications of Mathematics, Tome 17 (1972) no. 4, pp. 254-266

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MR
Transport equation for the function of the neutron density in a non-multiplying medium is discussed provided the initial distribution is given. The medium and source characteristics are considered generally to be functions of time. Existence and uniqueness for the initial value problem is proved and some previous results of the author are generalized. Besides, some consequences for the discussion of the behaviour of Knudsen's gas in a thermal bath are shown.
Transport equation for the function of the neutron density in a non-multiplying medium is discussed provided the initial distribution is given. The medium and source characteristics are considered generally to be functions of time. Existence and uniqueness for the initial value problem is proved and some previous results of the author are generalized. Besides, some consequences for the discussion of the behaviour of Knudsen's gas in a thermal bath are shown.
DOI : 10.21136/AM.1972.103417
Classification : 81-41 
Kyncl, Jan. Neutron transport initial value problem in non-multiplying medium. Applications of Mathematics, Tome 17 (1972) no. 4, pp. 254-266. doi: 10.21136/AM.1972.103417
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[1] J. Mika: The initial-value problem in neutron thermalization. Nukleonik 9 (1967), 303.

[2] J. T. Marti: Mathematical foundations of kinetics in neutron transport theory. Nukleonik 8 (1966), 159-163. | Zbl

[3] I. Vidav: Existence and uniqueness of nonnegative eigenfunctions of the Boltzmann operator. Journal of Math. Ann. and Appl. 22 (1968), 144-155. | DOI | MR | Zbl

[4] K. M. Case P. F. Zweifel: Existence and uniqueness theorems for the neutron transport equation. Journal of Math. Phys. 4, 11 (1963), 1376-85. | DOI | MR

[5] J. Kyncl: Initial condition in the theory of neutron transport. Aplikace matematiky 4, 17 (1972), 245. | MR

[6] V. Jarník: Integral calculus II. Prague, 1965.

[7] K. Andersen K. Shuller: J. Chem. Phys. 40 (1964), 633. | MR

[8] M. Grmela J. Kyncl: Relaxation of the uniform Knudsen gas coupled to a thermal bath. Can. Journ. of Phys. 47 (1959), 24, 2815-23. | DOI

[9] M. M. R. Williams: The slowing down and thermalization of neutrons. North-Holland Publishing Company, Amsterodam (1966).

[10] J. Potoček: Iterative methods. (reports lectured at Mathematical Institute of Charles University), Prague 1958-1959.

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