Far Eastern Mathematical Journal

To content of the issue


Optimal rigid control problem for one-dimensional MHD flow


V. E. Tsyba

2009, issue 1-2, P. 194–203


Abstract
An optimal rigid control problem for one-dimensional magneto hydrodynamic flow between parallel planes is considered. We use the external electromotive forces as a control function and minimize the functional corresponded with their work. An existence and uniqueness theorem is proved and optimal system is derived.

Keywords:
magneto hydrodynamic equation, rigid control, optimality system

Download the article (PDF-file)

References

[1] L. D. Landau, E. M. Lifshic, Teoreticheskaya fizika, t. 8, E'lektrodinamika sploshnyx sred, Fizmatlit, M., 2005.
[2] A. V. Fursikov, Optimal'noe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya, Nauchn. kniga, Novosibirsk, 1999.
[3] O. A. Ladyzhenskaya, V. A. Solonnikov, “Reshenie nekotoryx nestacionarnyx zadach magnitnoj gidrodinamiki dlya vyazkoj neszhimaemoj zhidkosti”, Tr. MIAN SSSR, 59, 1960, 174–187.
[4] M. Sermange, R. Temam, “Some mathematical questions related to the MHD equations”, Comm. Pure Appl. Math., 36 (1983), 635–664.
[5] V. Barbu, T. Havarneanu, C. Popa, S. S. Sritharan, “Exact controllability for magnetohydrodinamic equation”, Comm. Pure Appl. Math., 56 (2003), 732–783.
[6] J. M. Coron, “On the controllability of 2D incompressible perfect fluids”, J. Math. Pures. Appl., 75 (1996), 155–188.
[7] E. Fernandez-Cara, E. Zuazua, “The cost of approximate contollability for heat equation: The linear case”, Advances Diff. Eqs., 5 (2000), 465–514.
[8] D. L. Russell, “A unified boundary controllability theory for hiperbolic and parabolic partial differantial equations”, Studies in Appl. Math., 52 (1973), 189–221.
[9] A. V. Fursikov, O. Yu. Imanuvilov, Controllability of evolution equations, Lecture Notes Series 34, Research Institute of Mathematics, Global Analysis Research Center, Seoul National University, Korea, 1996.
[10] V. E. Cyba, “Mul'tiplikativnoe upravlenie MGD techeniem Gartmana”, Trudy instituta sistemnogo analiza, № 32(1), 2008, 87–100.
[11] V. E. Cyba, A. Yu. Chebotarev, “Asimptotika optimal'nogo upravleniya magnitogidrodinamicheskim techeniem”, Zh. vychisl. matem. i matem. fiz., 49:3 (2009), 482–489.
[12] Zh.-L. Lions, Optimal'noe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi, Mir, M., 1972.

To content of the issue