Quelques applications de la positivité en théorie du transport

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1. [1] Marek ( I.) .— Frobenius theory ofpositive operators : Comparison theorems and applications, Siam J. Appl. Math. Vol. 19, n°3 (1970) Zbl0219.47022MR415405
2. [2] Beals ( R.) .— An abstract treatment of some Forward-Backward problems of Transport and Scattering, J. Funct. Anal.34 (1979) pp. 1-20 Zbl0425.34067MR551106
3. [3] Kaper ( H.G.) .— Boundary value problems of mixed type arising in the kinetic theory of gases, Siam J. Math. Anal. Vol. 10, n°1 (1979) pp. 161-179 Zbl0414.45005MR516760
4. [4] Lions ( J.L.) .— A linear problem arising in kinetic theory of gases, dans Proc. Internat. Sympos. Inst. Mat. Univ. Federal Rio de Janeiro (1977) pp. 284-346, North-Holland Math. Studies30Amsterdam (1978) 
5. [5] Birkhoff ( G.) .- Positivity and criticality. In the Proceedings of Symposia in Applied Mathematics. Nuclear reactor theory, Am. Math. Soc. (1961) MR120814
6. [6] Greiner ( G.), Voigt ( J.) and Wolff ( M.) .— On the spectral bound of the generator of semigroups of positive operators, J. Op. Theory5 (1981) pp. 245-256 Zbl0469.47032MR617977
7. [7] Voigt ( J.) .— Positivity in time dependent linear transport theory, Acta Applicandæ Mathematicæ2 (1984) pp. 311-331 Zbl0579.47040MR753698
8. [8] Dautray ( R.) et Lions ( J.L.) .— Analyse mathématique et calcul numérique, Tome 3Masson, Paris (1985) Zbl0642.35001MR902802
9. [9] Mokhtar-Kharroubi ( M.) .— The time asymptotic behaviour and the compactness in neutron transport theory, Publication du Laboratoire d'Analyse Numérique. Paris. R. 86020 (1986) MR867550
10. [10] Kaper ( H.G.), Lekkerkerker ( C.G.) and Hejtmanek ( J.) .— Spectral methods in linear transport theory, Birkhäuser Verlag, Basel (1982) Zbl0498.47001MR685594
11. [11] Mokhtar-Kharroubi ( M.) .— Some spectral properties of the neutron transport operator in bounded geometries, Transport theory and statistical Physics16(7) (1987) pp. 935-958 Zbl0631.47001MR913932
12. [12] Mokhtar-Kharroubi ( M.) Thèse de 3ièmecycle, Univ. Paris 6 (1983) 
13. [13] Mokhtar-Kharroubi ( M.) .— Spectral theory of the neutron transport operator in bounded geometries, Transport theory and statistical Phisics16(4-6) (1987) pp. 467-502 Zbl0629.45011MR906915
14. [14] Mokhtar-Kharroubi ( M.) .— Spectral theory of the multigroup neutron transport operator, Eur. J. Mech. B/Fluids9, n° 2 (1990) pp. 197-222 Zbl0722.47060MR1096158
15. [15] J. Voigt .— Spectral properties of the neutron transport equation, J. Math. Anal. Appl. Vol. 106, n°1 (1985) Zbl0567.45002MR780325
16. [16] Aliprantis ( C.D.) and Burkinshaw ( O.) .— Positive compact operators on Banach lattices, Math. Z174 (1980) pp. 289-298 Zbl0425.46015MR593826
17. [17] Vidav ( I.) .— Existence and uniqueness of nonnegative eigenfunctions of the Boltzmann operator, J. Math. Anal. Appl.22 (1968) pp. 144-155 Zbl0155.19203MR230531
18. [18] Angelescu ( N.) and Protopopescu ( V.) .— On a problem in linear transport theory, Rev. Roumaine Phys.22 (1977) pp. 1055-1061 MR479215
19. [19] Victory ( H.D.) .— Jr. On linear integral operators with nonnegative kernels, J. Math. Anal. Appl. Vol 89, n°2 (1982) pp. 420-441 Zbl0496.47028MR677739
20. [20] Nagel ( R.) et al .— One parameter semigroups of positive operators, Lecture Notes in Mathematics1184, Springer Verlag (1986) Zbl0585.47030MR839450