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Reconstruction of controls in hyperbolic systems by Tikhonov’s method with nonsmooth stabilizers

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Abstract

The problem of reconstructing unknown controls in hyperbolic systems from the results of approximate observations of motions of these systems is considered. To solve the problem, Tikhonov’s method with a stabilizer containing the total time variation of the control is used. The use of such nondifferentiable stabilizer allows us to obtain more precise results in some cases than the approximation of the desired control in Lebesgue spaces. In particular, this method provides the piecewise uniform convergence of regularized approximations and makes possible the numerical reconstruction of the subtle structure of the desired control.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia

    A. I. Korotkii

  2. Ural Federal University, ul. Mira, 19, Yekaterinburg, 620002, Russia

    A. I. Korotkii & E. I. Gribanova

Authors
  1. A. I. Korotkii
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  2. E. I. Gribanova
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Correspondence to A. I. Korotkii.

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Original Russian Text © A.I. Korotkii, E.I.Gribanova, 2011, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2011, Vol. 17, No. 1.

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Korotkii, A.I., Gribanova, E.I. Reconstruction of controls in hyperbolic systems by Tikhonov’s method with nonsmooth stabilizers. Proc. Steklov Inst. Math. 275 (Suppl 1), 68–77 (2011). https://doi.org/10.1134/S0081543811090069

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  • DOI: https://doi.org/10.1134/S0081543811090069

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