Geodesic
Nontrivial solvability of the homogeneous Wiener–Hopf multiple integral equation in the conservative case and the Peierls equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 1, pp. 142-150 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We describe the process of constructing a positive solution of the homogeneous Wiener–Hopf integral equation in an octant in a special (conservative) case. Applying the obtained general results to the homogeneous stationary Peierls equation allows studying the behavior of the solutions of this equation for large argument values. These problems are particularly interesting in the theory of radiation transfer.
Keywords: Wiener–Hopf multiple integral equation, stationary Peierls equation, conservativity condition, asymptotic solution behavior. 
@article{TMF_2020_204_1_a8,
     author = {L. G. Arabadzhyan and G. L. Arabajyan},
     title = {Nontrivial solvability of the~homogeneous {Wiener{\textendash}Hopf} multiple integral equation in the~conservative case and {the~Peierls} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {142--150},
     year = {2020},
     volume = {204},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_204_1_a8/}
}
TY  - JOUR
AU  - L. G. Arabadzhyan
AU  - G. L. Arabajyan
TI  - Nontrivial solvability of the homogeneous Wiener–Hopf multiple integral equation in the conservative case and the Peierls equation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2020
SP  - 142
EP  - 150
VL  - 204
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2020_204_1_a8/
LA  - ru
ID  - TMF_2020_204_1_a8
ER  - 
%0 Journal Article
%A L. G. Arabadzhyan
%A G. L. Arabajyan
%T Nontrivial solvability of the homogeneous Wiener–Hopf multiple integral equation in the conservative case and the Peierls equation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2020
%P 142-150
%V 204
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2020_204_1_a8/
%G ru
%F TMF_2020_204_1_a8
L. G. Arabadzhyan; G. L. Arabajyan. Nontrivial solvability of the homogeneous Wiener–Hopf multiple integral equation in the conservative case and the Peierls equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 1, pp. 142-150. http://geodesic.mathdoc.fr/item/TMF_2020_204_1_a8/

[1] E. Hopf, Mathematical Problems of Radiative Equilibrium, Cambridge Tracts in Mathematics and Mathematical Physics, 31, Stechert-Hafner, New York, 1964 | MR

[2] V. A. Ambartsumyan, Nauchnye trudy, v. 1, ed. V. V. Sobolev, Izd-vo AN ArmSSR, Erevan, 1960

[3] S. Chandrasekar, Perenos luchistoi energii, IL, M., 1953 | MR | Zbl

[4] V. V. Sobolev, Rasseyanie sveta v atmosferakh planet, Nauka, M., 1972

[5] B. Devison, Teoriya perenosa neitronov, IL, M., 1960

[6] V. S. Vladimirov, Matematicheskie zadachi odnoskorostnoi teorii perenosa chastits, Tr. MIAN SSSR, 61, Izd-vo AN SSSR, M., 1961 | MR

[7] G. I. Marchuk, Metody rascheta yadernykh reaktorov, Atomizdat, M., 1961

[8] V. I. Gryn, “O sovmestnom opredelenii dvukh koeffitsientov trekhmernogo statsionarnogo uravneniya perenosa izlucheniya s izotropnym rasseyaniem”, Zhurn. vych. matem. i matem. fiziki, 33:1 (1993), 81–100 | MR | Zbl

[9] G. P. Klimov, Teoriya massovogo obsluzhivaniya, Iz-vo Mosk. un-ta, M., 2011

[10] L. G. Arabadzhyan, N. B. Engibaryan, “Uravneniya v svertkakh i nelineinye funktsionalnye uravneniya”, Itogi nauki i tekhn. Ser. Matem. anal., 22 (1984), 175–244 | DOI | MR | Zbl

[11] L. G. Arabadzhyan, “Odnorodnoe dvukratnoe uravnenie Vinera–Khopfa s simmetricheskim yadrom v konservativnom sluchae”, Matem. zametki, 106:1 (2019), 3–12 | DOI | DOI

[12] L. G. Arabadzhyan, N. B. Engibaryan, “O faktorizatsii kratnykh integralnykh operatorov Vinera–Khopfa”, Dokl. AN SSSR, 291:1 (1986), 11–14 | MR | Zbl

[13] L. G. Arabadzhyan, “O suschestvovanii netrivialnykh reshenii nekotorykh lineinykh i nelineinykh uravnenii tipa svertki”, Ukr. matem. zhurn., 41:12 (1989), 1587–1595 | DOI

[14] S. Lam, A. Leonard, “Milne's problem for two-dimentional transport in a quarter space”, J. Quant. Spectrosc. Radiat. Transfer, 11:6 (1971), 893–904 | DOI | MR

[15] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976 | MR