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Stability estimates for the solutions of control problems for the stationary magnetohydrodynamic equations

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Abstract

We study control problems for the stationary magnetohydrodynamic equations. In these problems, one has to find an unknown vector function occurring in the boundary condition for the magnetic field and the solution of the boundary value problem in question by minimizing a performance functional depending on the velocity and pressure. We derive new a priori estimates for the solutions of the original boundary value problem and the extremal problem and prove theorems on the local uniqueness and stability of solutions for specific performance functionals.

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Authors and Affiliations

  1. Far-Eastern Federal University, Vladivostok, Russia

    G. V. Alekseev & R. V. Brizitskii

  2. Institute for Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia

    G. V. Alekseev & R. V. Brizitskii

Authors
  1. G. V. Alekseev
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  2. R. V. Brizitskii
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Original Russian Text © G.V. Alekseev, R.V. Brizitskii, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 3, pp. 393–404.

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Alekseev, G.V., Brizitskii, R.V. Stability estimates for the solutions of control problems for the stationary magnetohydrodynamic equations. Diff Equat 48, 397–409 (2012). https://doi.org/10.1134/S0012266112030111

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