Geodesic
Formulas for an explicit solution of the model nonlocal problem associated with the ordinary transport equation
Matematičeskie zametki SVFU, Tome 24 (2017) no. 1, pp. 57-73 Cet article a éte moissonné depuis la source Math-Net.Ru

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A specific nonlocal problem for the multidimesional ordinary transport equation is studied. An additional condition for the time averages is given. The theorem of existence and uniqueness of solution is obtained. We show that the solution could be found constructively, explicitly, and in a finite number of iterations.
Mots-clés : transport equation
Keywords: nonlocal problem, resolving formula. 
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I. V. Tikhonov; V. N. Son Tung. Formulas for an explicit solution of the model nonlocal problem associated with the ordinary transport equation. Matematičeskie zametki SVFU, Tome 24 (2017) no. 1, pp. 57-73. http://geodesic.mathdoc.fr/item/SVFU_2017_24_1_a5/

[1] Kaper H. G., Lekkerkerker C. G., and Hejtmanek J., Spectral methods in linear transport theory, Birkhäuser, Basel, 1982 | MR | Zbl

[2] Reed M. and Simon B, Methods of Modern Mathematical Physics, v. 3, Scattering Theory, Mir, Moscow, 1982 | MR

[3] Engel K.-J. and Nagel R., One-parameter semigroups for linear evolution equations, Springer-Verl., New York, 2000 | MR | Zbl

[4] Jörgens K., “An asymptotic expansion in the theory of neutron transport”, Commun. Pure Appl. Math., 11:2 (1958), 219–242 | DOI | MR | Zbl

[5] Greiner G., “Spectral properties and asymptotic behavior of the linear transport equation”, Math. Z., 185:2 (1958), 167–177 | DOI | MR

[6] Prilepko A. I., “Inverse problems of potential theory (elliptic, parabolic, hyperbolic, and transport equations)”, Math. Notes, 14 (1974), 990-996 | DOI | MR | Zbl

[7] Prilepko A. I. and Ivankov A. L., “Inverse problems for determining the coefficient, the scattering indicatrix and the right-hand side of a time-dependent multiple-speed transport equation”, Differ. Equations, 21 (1985), 598–609 | MR | Zbl

[8] Orlovskij D. G. and Prilepko A. I., “Some inverse problems for the linearized Boltzmann equation”, U.S.S.R. Comput. Math. Math. Phys., 27:6 (1987), 58–65 | DOI | MR | Zbl

[9] Prilepko A. I. and Volkov N. P., “Inverse problems of finding parameters of a nonstationary kinetic transfer equation from supplementary information on traces of the unknown function”, Differ. Equations, 24:1 (1988), 107–115 | MR | Zbl

[10] Tikhonov I. V., “Well-posedness of an inverse problem with final overdetermination for the nonstationary transport equation”, Mosc. Univ. Comput. Math. Cybern., 1995, no. 1, 51–57 | MR | Zbl

[11] Tikhonov I. V., “Solvability of a problem with a nonlocal integral condition for a differential equation in a Banach space”, Differ. Equations, 34:6 (1998), 841–844 | MR | Zbl

[12] Tikhonov I. V., “Uniqueness theorems in linear nonlocal problems for abstract differential equations”, Izv. Math., 67:2 (2003), 333—363 | DOI | MR | Zbl

[13] Arutyunov A. V, Lectures on Convex and Many-Valued Analysis, Fizmatlit, Moscow, 2014

[14] J. Soviet Math., 54:4 (1991), 1042–1129 | DOI | MR | Zbl