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Generalized control with compact support of wave equation with variable coefficients

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Abstract

A new approach for investigating the exact controllability of the one-dimensional wave equation with variable coefficients on a finite interval, subjected to boundary conditions of mixed type, and to determine the controls explicitly is suggested. The control process is carried out either by one of the boundary functions or by the right hand side of the equation. The method of compactly supported control is generalized and applied for reducing the problem to a countable system of linear integral constraints. That system is treated as problem of moments. \(L^1\) and \(L^2\)-optimal controls are found explicitly, necessary and sufficient conditions of exact controllability are obtained.

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Acknowledgments

We would like to thank Prof. Ed. Grigoryan for his idea and R. Ghazaryan for her support. We thank as well the referees for their careful reading and suggested improvements.

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Authors and Affiliations

  1. Yerevan State University, 1 Alex Manoogian, 0025, Yerevan, Armenia

    Asatur Zh. Khurshudyan

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  1. Asatur Zh. Khurshudyan
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Correspondence to Asatur Zh. Khurshudyan.

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To the blessed memory of innocent victims of Armenian Genocide (1915) is dedicated.

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Khurshudyan, A.Z. Generalized control with compact support of wave equation with variable coefficients. Int. J. Dynam. Control 4, 447–455 (2016). https://doi.org/10.1007/s40435-015-0148-3

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  • DOI: https://doi.org/10.1007/s40435-015-0148-3

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