On three problems of neutron transport theory

Jan Kyncl

Aplikace matematiky (1986)

  • Volume: 31, Issue: 6, page 441-460
  • ISSN: 0862-7940

Abstract

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In this paper, the initial-value problem, the problem of asymptotic time behaviour of its solution and the problem of criticality are studied in the case of linear Boltzmann equation for both finite and infinite media. Space of functions where these problems are solved is chosen in such a vay that the range of physical situations considered may be so wide as possible. As mathematical apparatus the theory of positive bounded operators and of semigroups are applied. Main results are summarized in three basic theorems.

How to cite

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Kyncl, Jan. "On three problems of neutron transport theory." Aplikace matematiky 31.6 (1986): 441-460. <http://eudml.org/doc/15469>.

@article{Kyncl1986,
abstract = {In this paper, the initial-value problem, the problem of asymptotic time behaviour of its solution and the problem of criticality are studied in the case of linear Boltzmann equation for both finite and infinite media. Space of functions where these problems are solved is chosen in such a vay that the range of physical situations considered may be so wide as possible. As mathematical apparatus the theory of positive bounded operators and of semigroups are applied. Main results are summarized in three basic theorems.},
author = {Kyncl, Jan},
journal = {Aplikace matematiky},
keywords = {neutron flux; analytical solution; cross sections; semigroup of operators; asymptotic behaviour; linear Boltzmann equation; neutron transport; initial value problem; non-negative asymptotic solution; critical system; neutron flux; analytical solution; cross sections; semigroup of operators; asymptotic behaviour; linear Boltzmann equation; neutron transport; initial value problem; non-negative asymptotic solution; critical system},
language = {eng},
number = {6},
pages = {441-460},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On three problems of neutron transport theory},
url = {http://eudml.org/doc/15469},
volume = {31},
year = {1986},
}

TY - JOUR
AU - Kyncl, Jan
TI - On three problems of neutron transport theory
JO - Aplikace matematiky
PY - 1986
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 31
IS - 6
SP - 441
EP - 460
AB - In this paper, the initial-value problem, the problem of asymptotic time behaviour of its solution and the problem of criticality are studied in the case of linear Boltzmann equation for both finite and infinite media. Space of functions where these problems are solved is chosen in such a vay that the range of physical situations considered may be so wide as possible. As mathematical apparatus the theory of positive bounded operators and of semigroups are applied. Main results are summarized in three basic theorems.
LA - eng
KW - neutron flux; analytical solution; cross sections; semigroup of operators; asymptotic behaviour; linear Boltzmann equation; neutron transport; initial value problem; non-negative asymptotic solution; critical system; neutron flux; analytical solution; cross sections; semigroup of operators; asymptotic behaviour; linear Boltzmann equation; neutron transport; initial value problem; non-negative asymptotic solution; critical system
UR - http://eudml.org/doc/15469
ER -

References

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  1. M. Borysiewicz, J. Mika, 10.1016/0022-247X(69)90193-0, J. Math. Anal. 26 (1969) 461. (1969) DOI10.1016/0022-247X(69)90193-0
  2. E. W. Larsen, P. F. Zweifel, 10.1063/1.1666570, J. Math. Phys. 15 (1974) 1987. (1974) MR0359648DOI10.1063/1.1666570
  3. J. Mika, The initial-value problem in neutron thermalization, Neukleonik 9 (1967) 303. (1967) 
  4. M G. Krein, M. A. Rutman, Linear operators leaving invariant a cone in a Banach space, Usp. Mat. Nauk III, 3 (1948) (Russian). (1948) Zbl0030.12902MR0027128
  5. I. Vidav, 10.1016/0022-247X(68)90166-2, J. Math. Anal. Appl. 22 (1968) 144. (1968) Zbl0155.19203MR0230531DOI10.1016/0022-247X(68)90166-2
  6. J. Mika, 10.1016/0022-4073(71)90062-8, J. Quant. Spectroscop. Radiat. Transfer 11 (1971) 879. (1971) MR0408663DOI10.1016/0022-4073(71)90062-8
  7. I. Marek, Some mathematical problems of the fast nuclear reactor theory, Apl. Mat. 8 (1963) 442 (Russian). (1963) 
  8. H. G. Kaper C. G. Lekkerkerker, J. Hejtmanek, Spectral methods in linear transport theory, Stuttgart 1982. (1982) MR0685594
  9. J. Kyncl, The initial-value problem in the theory of neutron transport, Kernenergie 19 (1976) 210. (1976) 
  10. K. Yosida, Functional analysis, Moscow 1967. (1967) Zbl0152.32102MR0225130
  11. N. Dunford, J. T. Schwarz, Linear operators, New York 1958. (1958) 

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