| Title:
|
Fundamental decay mode and asymptotic behaviour of positive semigroups (English) |
| Author:
|
Marek, Ivo |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
30 |
| Issue:
|
4 |
| Year:
|
1980 |
| Pages:
|
579-590 |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
34G10 |
| MSC:
|
47D05 |
| MSC:
|
82A70 |
| idZBL:
|
Zbl 0468.47025 |
| idMR:
|
MR592321 |
| DOI:
|
10.21136/CMJ.1980.101706 |
| . |
| Date available:
|
2008-06-09T14:41:16Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101706 |
| . |
| Reference:
|
[1] Albertoni S., Montagnini В.: On the spectrum of neutron transport equation in finite bodies.J. Math. Anal. Appl. 13, 19-48, 1966. Zbl 0144.48304, MR 0189741, 10.1016/0022-247X(66)90073-4 |
| Reference:
|
[2] Hille E., Phillips R. S.: Functional Analysis and Semigroups.Revised Edition, American Math. Soc. Colloq. Publ. Vol. XXXI, Providence, 1957. Zbl 0078.10004, MR 0089373 |
| Reference:
|
[3] Jörgens K.: On asymptotic expansion in the theory of neutron transport.Comm. Pure Appl. Math. 11, 219-242, 1957. MR 0103419, 10.1002/cpa.3160110206 |
| Reference:
|
[4] Kaper H. G.: A collection of problems in transport theory.Transport Theory and Stat. Physics 4, 13, 125-134, 1975. MR 0465011, 10.1080/00411457508214535 |
| Reference:
|
[5] Krein M. G., Rutman M. A.: Linear operators leaving invariant a cone in a Banach space.Uspekhi mat. nauk. III, N1, 3 - 95, 1948, (Russian). English translation in Amer. Math. Soc. Translations No. 26, pp. 128, 1950. Zbl 0030.12902, MR 0027128 |
| Reference:
|
[6] Larsen E. W., Zweifel P. F.: On the spectrum of the linear transport operator.J. Math.-Phys. 15, 1987-1997, 1974. MR 0359648, 10.1063/1.1666570 |
| Reference:
|
[7] Lehner J.: An unsymmetric operator arising in the theory of neutron diffusion.Comm. Pure Appl. Math. 9, 487-497, 1956. Zbl 0070.45302, MR 0084097, 10.1002/cpa.3160090320 |
| Reference:
|
[8] Lehner J., Wing G. M.: On the spectrum of an unsymmetric operator arising in the transport theory of neutrons.Comm. Pure Appl. Math. 8, 217-234, 1955. Zbl 0064.23004, MR 0070038 |
| Reference:
|
[9] Lehner J., Wing G. M.: Solution of the linearized Boltzman equation for the slab geometry.Duke Math. J. 23, 125-142, 1956. MR 0079214 |
| Reference:
|
[10] Marek I.: Frobenius theory of positive operators. Comparison theorems and applications.SIAM J. Appl. Math. 19, 607-628, 1970. Zbl 0219.47022, MR 0415405, 10.1137/0119060 |
| Reference:
|
[11] Marek I.: On some spectral properties of Radon-Nikolskii operators and their generalizations.Comment. Math. Univ. Carol. 3: 1, 20-30, 1962. MR 0144216 |
| Reference:
|
[12] Niiro F., Sawashima I.: On spectral properties of positive irreducible operators in an arbitrary Banach lattice and problems of H. H. Schaefer.Sci. Papers College Gen. Educ., Univ. of Tokyo, 16, 145-183, 1966. MR 0205084 |
| Reference:
|
[13] Sawashima I.: Spectral properties of some positive operators.Natur. Sci. Rep. Ochanomizu Univ. 15. 55-64, 1964. Zbl 0138.07801, MR 0187096 |
| Reference:
|
[14] Schaefer H. H.: Banach Lattices and Positive Operators.Springer Verlag, Berlin-Heidelberg-New York, 1974. Zbl 0296.47023, MR 0423039 |
| Reference:
|
[15] Shikhov S. В.: Lectures in Mathematical Theory of Reactors. I. Linear Theory.Atomizdat, Moscow, 1973 (Russian). |
| Reference:
|
[16] Shizuta Y.: On the classical solutions of the Boltzmann equation.Preprint 1977. MR 0720591 |
| Reference:
|
[17] Taylor A. E.: Introduction to Functional Analysis.J. Wiley Publ., New York, 1958. Zbl 0081.10202, MR 0098966 |
| Reference:
|
[18] Ukai S.: On the existence of global solutions of mixed problem from non-linear Boltzmann equation.Proc. Japan Acad. 50, 179-184, 1974. MR 0363332 |
| Reference:
|
[19] Vidav I.: Existence and uniqueness of non-negative eigenfunctions of the Boltzmann operator.J. Math. Anal. Appl. 22, 144-155, 1968. MR 0230531, 10.1016/0022-247X(68)90166-2 |
| Reference:
|
[20] Vidav I.: Spectra of perturbed semigroups with applications to transport theory.J. Math. Anal. Appl. 30, 264-279, 1970. Zbl 0195.13704, MR 0259662, 10.1016/0022-247X(70)90160-5 |
| Reference:
|
[21] Wing G. M.: An Introduction to Transport Theory.J. Wiley Publ., New York, 1962. MR 0155646 |
| . |
