| Title:
|
On three problems of neutron transport theory (English) |
| Author:
|
Kyncl, Jan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
31 |
| Issue:
|
6 |
| Year:
|
1986 |
| Pages:
|
441-460 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
neutron flux |
| Keyword:
|
analytical solution |
| Keyword:
|
cross sections |
| Keyword:
|
semigroup of operators |
| Keyword:
|
asymptotic behaviour |
| Keyword:
|
linear Boltzmann equation |
| Keyword:
|
neutron transport |
| Keyword:
|
initial value problem |
| Keyword:
|
non-negative asymptotic solution |
| Keyword:
|
critical system |
| MSC:
|
45K05 |
| MSC:
|
45M05 |
| MSC:
|
82A75 |
| MSC:
|
82C70 |
| idZBL:
|
Zbl 0615.45012 |
| idMR:
|
MR0870481 |
| DOI:
|
10.21136/AM.1986.104223 |
| . |
| Date available:
|
2008-05-20T18:31:05Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104223 |
| . |
| Reference:
|
[1] M. Borysiewicz, J. Mika: Time behaviour of thermal neutrons in moderating media.J. Math. Anal. 26 (1969) 461. 10.1016/0022-247X(69)90193-0 |
| Reference:
|
[2] E. W. Larsen, P. F. Zweifel: On the spectrum of linear transport operator.J. Math. Phys. 15 (1974) 1987. MR 0359648, 10.1063/1.1666570 |
| Reference:
|
[3] J. Mika: The initial-value problem in neutron thermalization.Neukleonik 9 (1967) 303. |
| Reference:
|
[4] M G. Krein, M. A. Rutman: Linear operators leaving invariant a cone in a Banach space.Usp. Mat. Nauk III, 3 (1948) (Russian). Zbl 0030.12902, MR 0027128 |
| Reference:
|
[5] I. Vidav: Existence and uniqueness of nonnegative eigenfunctions of the Boltzmann operator.J. Math. Anal. Appl. 22 (1968) 144. Zbl 0155.19203, MR 0230531, 10.1016/0022-247X(68)90166-2 |
| Reference:
|
[6] J. Mika: Fundamental eigenvalues of the linear transport equation.J. Quant. Spectroscop. Radiat. Transfer 11 (1971) 879. MR 0408663, 10.1016/0022-4073(71)90062-8 |
| Reference:
|
[7] I. Marek: Some mathematical problems of the fast nuclear reactor theory.Apl. Mat. 8 (1963) 442 (Russian). |
| Reference:
|
[8] H. G. Kaper C. G. Lekkerkerker, J. Hejtmanek: Spectral methods in linear transport theory.Stuttgart 1982. MR 0685594 |
| Reference:
|
[9] J. Kyncl: The initial-value problem in the theory of neutron transport.Kernenergie 19 (1976) 210. |
| Reference:
|
[10] K. Yosida: Functional analysis.Moscow 1967. Zbl 0152.32102, MR 0225130 |
| Reference:
|
[11] N. Dunford, J. T. Schwarz: Linear operators.New York 1958. |
| . |
