Far Eastern Mathematical Journal

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Analysis of inverse extremal problems for the non-linear stationary mass-transfer equations


G. V. Alekseev, E. A. Adomavichus

2002, issue 1, Ñ. 79–92


Abstract
This work deals with inverse extremal problems for the non-linear stationary mass-transfer equations. The states of system are the velocity, pressure of fluid and concentration of substance. The control problem consists in minimizing one of two cost functionals. Existence of optimal solutions is proved and existence of Lagrange multipliers is verified. The optimality conditions for these problems are derived. Regularity solutions of Lagrange multipliers is studied and sufficient conditions of uniqueness of the inverse extremal problems for the concrete functional are derived.

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References

[1] F. Abergel and E. Casas, “Some optimal control problems of multistate equation appearing in fluid mechanics”, Math. Modeling Numer. Anal., 27 (1993), 223–247.
[2] K. Ito, “Boundary temperature control for thermally coupled Navier-Stokes equations”, Int. Ser. Numer. Math., 118 (1994), 211–230.
[3] G. V. Alekseev, Teoreticheskij analiz stacionarnyx zadach granichnogo upravleniya dlya uravnenij teplovoj konvekcii, Preprint ¹ 16. IPM DVO RAN, Dal'nauka, Vladivostok, 1996, 64 s.
[4] G. V. Alekseev, “Stacionarnye zadachi granichnogo upravleniya dlya uravnenij teplovoj konvekcii”, Dokl. RAN, 362:2 (1998), 174–177.
[5] G. V. Alekseev, “Razreshimost' stacionarnyx zadach granichnogo upravleniya dlya uravnenij teplovoj konvekcii”, Sib. mat. zhurn., 39:5 (1998), 982–998.
[6] G. V. Alekseev, D. A. Tereshko, “Solvability of the inverse extremal problem for the incompressible heatconducting fluid equations”, J. Inverse Ill-posed Problems., 6:6 (1998), 521–562.
[7] G. V. Alekseev, D. A. Tereshko, “Stacionarnye zadachi optimal'nogo upravleniya dlya uravnenij vyazkoj teploprovodnoj zhidkosti”, Sib. zh. ind. mat., 1:2 (1998), 24–44.
[8] E'. A. Adomavichyus, “O razreshimosti nekotoryx e'kstremal'nyx zadach dlya stacionarnyx uravnenij teplovoj konvekcii”, Dal'nevostochnyj matem. cb., 5, 1998, 74–85.
[9] K. Ito and S. S. Ravindran, “Optimal control of thermally convected fluid flows”, SIAM J. Sci. Comput., 19:6 (1998), 1847–1869.
[10] Anca Capatina and Ruxandra Stavre, “A control problem in bioconvective flow”, J. Math. Kyoto Univ., 37:4 (1998), 585–595.
[11] H. C. Lee and O. Yu. Imanuvilov, “Analysis of optimal control problems for the 2-D stationary Boussinesq equations”, J. Math. Anal. Appl., 242:2 (2000), 191–211.
[12] E'. A. Adomavichyus, G. V. Alekseev, Teoreticheskij analiz obratnyx e'kstremal'nyx zadach dlya stacionarnyx uravnenij massoperenosa, Preprint ¹ 7. IPM DVO RAN, Dal'nauka, Vladivostok, 1999, 44 s.
[13] E'. A. Adomavichyus, G. V. Alekseev, “O razreshimosti neodnorodnyx kraevyx zadach dlya stacionarnyx uravnenij massoperenosa”, Dal'nevostochnyj mat. zhurn., 2001, ¹ 2, 138–153.
[14] A. D. Ioffe, V. M. Tixomirov, Teoriya e'kstremal'nyx zadach, Nauka, M., 1974, 480 s.
[15] E'. A. Adomavichyus, G. V. Alekseev, Teoreticheskij analiz obratnyx e'kstremal'nyx zadach dlya stacionarnyx uravnenij massoperenosa II, Preprint ¹ 18. IPM DVO RAN, Dal'nauka, Vladivostok, 1999, 36 s.
[16] G. V. Alekseev, Teoreticheskij analiz obratnyx e'kstremal'nyx zadach dlya stacionarnyx uravnenij teplomassoperenosa, Preprint. IPM DVO RAN, Dal'nauka, Vladivostok, 2000.
[17] M. D. Gunzburger, L. Hou and T. P. Svobodny, “Boundary velocity control of incompressible flow with application to viscous drag reduction”, SIAM J. Contr. Optim., 30:1 (1992), 167–181.

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