Far Eastern Mathematical Journal

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On stability of solutions of extremum problems for stationary equations of mass transfer


G. V. Alekseev, O. V. Soboleva

2009, issue 1-2, Ń. 5–14


Abstract
Inverse extremum problems for stationary equations of mass transfer are considered. Heat flux through the part of the boundary and the volume impurity source density play the role of controls. The mean quadratic integral deviation of the velocity or vorticity field from the given field in a part of the domain is chosen as the cost functional. Sufficient conditions to input data are established, which provide the uniqueness and stability of solutions.

Keywords:
mass transfer, extremum problems, optimality system, stability

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References

[1] Gunzburger M.D., Hou L., Svobodny T.P., “The approximation of boundary control problems for fluid flows with an application to control by heating and cooling”, Comput. Fluids, 22 (1993), 239–251.
[2] Ito K., Ravindran S.S., “Optimal control of thermally convected fluid flows”, SIAM J. Sci. Comput., 19:6 (1998), 1847–1869.
[3] Alekseev G.V., “Razreshimost' stacionarnyx zadach granichnogo upravleniya dlya uravnenij teplovoj konvekcii”, Sib. mat. zhurn., 39:5 (1998), 982–998.
[4] Lee N.-C., Imanuvilov O.Yu., “Analysis of optimal control problems for the 2-D stationary Boussinesq equations”, J. Math. Anal. Appl., 242 (2000), 191–211.
[5] Alekseev G.V., “Razreshimost' obratnyx e'kstremal'nyx zadach dlya stacionarnyx uravnenij teplomassoperenosa”, Sib. mat. zhurn., 42:5 (2001), 971–991.
[6] Alekseev G.V., “Obratnye e'kstremal'nye zadachi dlya stacionarnyx uravnenij teorii massoperenosa”, Zhurn. vychisl. matem. matem. fiz., 42:3 (2002), 380–394.
[7] Alekseev G.V., “Edinstvennost' i ustojchivost' v koe'fficientnyx obratnyx e'kstremal'nyx zadachax dlya stacionarnoj modeli massoperenosa”, Dokl. AN, 416:6 (2007), 750–753.
[8] Alekseev G.V., “Koe'fficientnye obratnye e'kstremal'nye zadachi dlya stacionarnyx uravnenij teplomassoperenosa”, Zhurn. vychisl. matem. matem. fiziki, 47:6 (2007), 1055–1076.
[9] Alekseev G.V., Soboleva O.V., Tereshko D.A., “Zadachi identifikacii dlya stacionarnoj modeli massoperenosa”, Prikl. mex. texn. fiz., 49:4 (2008), 24–35.
[10] Alekseev G.V., Tereshko D.A., Analiz i optimizaciya v gidrodinamike vyazkoj zhidkosti, Dal'nauka, Vladivostok, 2008.

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