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Analysis and optimization in problems of cloaking of material bodies for the Maxwell equations

  • Partial Differential Equations
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Abstract

We consider control problems for the 3D Maxwell equations describing electromagnetic wave scattering in an unbounded inhomogeneous medium that contains a permeable isotropic obstacle with cloaking boundary. Such problems arise when studying cloaking problems by the optimization method. The boundary coefficient occurring in the impedance boundary condition plays the role of a control. We study the solvability of the control problem and derive optimality systems that describe necessary conditions for the extremum. By analyzing the constructed optimality systems, we justify sufficient conditions imposed on the input data providing the uniqueness and stability of optimal solutions.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia

    G. V. Alekseev

  2. Far Eastern Federal University, Vladivostok, Russia

    G. V. Alekseev

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  1. G. V. Alekseev
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Correspondence to G. V. Alekseev.

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Original Russian Text © G.V. Alekseev, 2016, published in Differentsial’nye Uravneniya, 2016, Vol. 52, No. 3, pp. 366–377.

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Alekseev, G.V. Analysis and optimization in problems of cloaking of material bodies for the Maxwell equations. Diff Equat 52, 361–372 (2016). https://doi.org/10.1134/S0012266116030101

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  • DOI: https://doi.org/10.1134/S0012266116030101

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