| Title:
|
Relaxation lengths and non-negative solutions in neutron transport (English) |
| Author:
|
Kyncl, Jan |
| Author:
|
Marek, Ivo |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
22 |
| Issue:
|
1 |
| Year:
|
1977 |
| Pages:
|
1-13 |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Keyword:
|
equation of neutron transport |
| Keyword:
|
fredholm theory |
| Keyword:
|
integro-partial differential equations |
| Keyword:
|
spectral theory |
| Keyword:
|
existence of nonnegative eigenfunctions |
| MSC:
|
45B05 |
| MSC:
|
45C05 |
| MSC:
|
45K05 |
| MSC:
|
76P05 |
| MSC:
|
82C70 |
| idZBL:
|
Zbl 0399.45016 |
| idMR:
|
MR0426731 |
| DOI:
|
10.21136/AM.1977.103674 |
| . |
| Date available:
|
2008-05-20T18:06:20Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103674 |
| . |
| Reference:
|
[1] M. Borysewicz J. Mika: Time behavior of thermal neutrons in moderator media.CNEN Documents CEC (68), 1 Bologna (1968). |
| Reference:
|
[2] K. M. Case: Elementary solutions of the transport equation and their applications.Ann. Phys. 9 (1960), 1-23. Zbl 0087.42301, MR 0109471, 10.1016/0003-4916(60)90060-9 |
| Reference:
|
[3] C. Cercignani: Unsteady solutions of the kinetic models with velocity-dependent collision frequency.Ann. Phys. 40 (1966), 454 - 468. MR 0219288, 10.1016/0003-4916(66)90145-X |
| Reference:
|
[4] B. Davison: Milne problem in a multiplying medium with a linearly anisotropic scattering.Canadian Report CRT 358 (1946). |
| Reference:
|
[5] B. Davison: Neutron Transport Theory.Oxford University Press, London 1957. Zbl 0077.22505, MR 0095716 |
| Reference:
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[6] J. J. Duderstadt: Theory of the propagation of the plane-wave disturbances in a distribution of thermal neutrons.J. Math. Phys. 10 (1969), 266-276. MR 0237159, 10.1063/1.1664842 |
| Reference:
|
[7] N. Dunford J. T. Schwartz: Linear operators.Part I. Interscience Publ. New York 1957. |
| Reference:
|
[8] L. C. Gokhberg M. G. Krein: The basic propositions on defect numbers, root numbers and indices of linear operators.Usp. mat. nauk XII (1957), 43-118 (Russian). |
| Reference:
|
[9] H. Grad: Asymptotic theory of the Boltzmann equation.I. Proceedings of the Third Intern. Symp. Rarefied Gas Dynamics, Vol. I, Academic Press, New York -London, 1963, pp. 26-59. Zbl 0115.45006, MR 0156656 |
| Reference:
|
[10] E. Hecke: Über die Integralgleichung der kinetischen Gastheorie.Math. Zeitschrift 12 (1922), 277-286. |
| Reference:
|
[11] S. Kaplan: Properties of the relaxation lengths in $P_L$, double $P_L$ and angle-space synthetic approximations.Bull. Sci. Eng. 28 (1967), 456. |
| Reference:
|
[12] T. Kato: Perturbation Theory for Linear Operators.Springer-Verlag, Berlin-Heidelberg- New York 1966. Zbl 0148.12601, MR 0203473 |
| Reference:
|
[13] M. G. Krein M. A. Rutman: Linear operators leawing invariant a cone in a Banach space.Usp. mat. Nauk III (1948), N 1, 3 - 95 (Russian), English translation in the Translations of the AMS, Vol. 26 (1952). MR 0027128 |
| Reference:
|
[14] I. Kuščer N. Corngold: Discrete relaxation times in neutron thermalization.Phys. Rev. 139 (1965), A981-990; 140 (1965), A85. 10.1103/PhysRev.139.A981 |
| Reference:
|
[15] I. Kuščer I. Vidav: On the spectrum of relaxation lengths of neutron distributions in a moderator.J. Math. Anal. Appl. 25 (1969), 80-92. 10.1016/0022-247X(69)90214-5 |
| Reference:
|
[16] I. Marek: Frobenius theory of positive operators. Comparison theorems and applications.SIAM J. Appl. Math. 19 (1970), 607-628. Zbl 0219.47022, MR 0415405, 10.1137/0119060 |
| Reference:
|
[17] I. Marek: On Fredholm points of compactly perturbed bounded linear operators.Acta Univ. Carol. - Mathematica et Physica Vol. 17, (1976) No. 1, 65 - 72. MR 0423106 |
| Reference:
|
[18] I. Marek: On some spectral properties of Radon-Nikolskii operators and their generalizations.Comment. Math. Univ. Carol. 3, 1 (1962), 20-30. MR 0144216 |
| Reference:
|
[19] J. Mika: Neutron transport with anisotropic scattering.Nucl. Sd. Eng. 11 (1961), 415 - 427. 10.13182/NSE61-1 |
| Reference:
|
[20] B. Montagnini M. L. Demuru: Complete continuity of the free gas scattering operator in neutron thermalization theory.J. Math. Anal. Appl. 12 (1965), 49-57. MR 0186322, 10.1016/0022-247X(65)90052-1 |
| Reference:
|
[21] W. Rudin: Functional Analysis.McGraw-Hill Co. New York, 1973. Zbl 0253.46001, MR 0365062 |
| Reference:
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[22] I. Sawashima: On spectral properties of some positive operators.Natur. Sci. Rep. Ochanomizu Univ. 15 (1969), 55-66. MR 0187096 |
| Reference:
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[23] V. F. Turchin: Thermal Neutrons.Gosatomizdat, Moscow 1963 (Russian). |
| Reference:
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[24] L. Van Hove: Correlations in space and time and Born approximation scattering in systems of interacting particles.Phys. Rev. 95 (1954), 249. Zbl 0056.44205, MR 0063964, 10.1103/PhysRev.95.249 |
| Reference:
|
[25] A. M. Weinberg E. P. Wigner: The Physical Theory of Neutron Chain Reactors.Chicago University Press, Chicago 1958. MR 0113336 |
| Reference:
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[26] M. M. R. Williams: The Slowing Down and Thermalization of Neutrons.North-Holland Publ. Company, Amsterdam 1966. |
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|
[27] R. Zelazny: Exact solution of a critical problem for a slab.J. Math. Phys. 2 (1961), 538-542. Zbl 0102.43102, MR 0129922, 10.1063/1.1703738 |
| . |
