Geodesic
Existence and uniqueness of the solution of the adjoint system in one problem of
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1065-1079

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In this paper the problem of optimal control of mathematical model of a non-adiabatic tubular reactor is considered. The proof of existence and uniqueness of the solution of the adjoint system in weight Hölder classes is carried out.
Keywords: mathematical model, chemical reactor, optimal control, functional, necessary condition of an optimality, maximum principle of Pontryagin, the adjoint system. 
K. S. Musabekov. Existence and uniqueness of the solution of the adjoint system in one problem of. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1065-1079. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a99/
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[1] L.S. Pontryagin, V.G., R.V. Gamkrelidze, E.F. Mishchenko, The Mathematical Theory of Optimal Processes, Wiley Sons, New York, 1962 | MR | Zbl

[2] V.A.Solonnikov, “About boundary value Problems and linear parabolic common view differential equations systems”, Proceedings of the Steklov Inst. Math., 83, 1965, 3–162 (In Russian) | MR

[3] V.S. Belonosov, T.I. Zelenyak, Nonlocal problems in the theory of quasilinear parabolic equations, Novosib. Gos. Univ., Novosibirsk, 1975 (In Russian) | MR

[4] V.S. Belonosov, “Decision assessment of parabolic systems in Hölder's weight class in some use”, Mathematical Sb., 110(152):2 (1979), 163–188 (In Russian) | MR | Zbl

[5] C. Georgakis, R. Aris, N.R. Amundson, “Studies in the control of Tubular Reactors”, Chemical Engineering Sience, 32:11 (1977), 1359–1387 | DOI

[6] K.S. Mussabekov, “Existence theorems for the solution in a problem of optimal control of a chemical reactor”, Controllable processes and optimization, Controllable systems, 22, Novosibirsk, 1982, 30–50 (in Russian)

[7] O.A. Ladyzhenskaya, V.A. Solonnikov, N.N. Uralcheva, Linear and kvazilinear equations parabolic type, Nauka, M., 1967 (in Russian) | MR

[8] K.S. Musabekov, “Existence of Optimal Control for regularized problem with Phase constraint”, Journal of Mathematical Sciences, 186:3 (2012), 466–477 | DOI | MR

[9] K.S. Musabekov, “Penalty Method for Optimal Control Problem with Phase constraint”, Journal of Mathematical Sciences, 203:4 (2014), 558–569 | DOI | MR

[10] E.A. Coddington, N. Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York, 1955 | MR | Zbl

[11] J. Leray, J. Schauder, “Topologie et equations fonctionnelles”, Ann. Sci l'Ecole Norm. Sup., 51 (1934), 45–78 | DOI | MR