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On an Optimal Control Problem for the Wave Equation in One Space Dimension Controlled by Third Type Boundary Data

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Progress in Partial Differential Equations

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 44))

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Abstract

In the present paper we study the boundary control by the third boundary condition on the left end of a string, the right end being fixed. An optimality criterion based on the minimization of an integral of a linear combination of the control itself and its antiderivative raised to an arbitrary power p≥1 is established. A method is developed permitting one to find a control satisfying this optimality criterion and write it out in the explicit form. The optimal control for p>1 is proved. Thereby proposed optimality criterion uniquely determines the optimal solution of boundary control problem under consideration.

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Author information

Authors and Affiliations

  1. Lomonosov Moscow State University, Leninskie Gory, Moscow, 119991, Russian Federation

    Alexey Nikitin

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  1. Alexey Nikitin
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Correspondence to Alexey Nikitin .

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Editors and Affiliations

  1. Institut of Applied Analysis, TU Bergakademie Freiberg, Prüferstr. 9, Freiberg, 09596, Sachsen, Germany

    Michael Reissig

  2. Department of Mathematics, Imperial College London, 180 Queen's Gate, London, SW7 2AZ, United Kingdom

    Michael Ruzhansky

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Nikitin, A. (2013). On an Optimal Control Problem for the Wave Equation in One Space Dimension Controlled by Third Type Boundary Data. In: Reissig, M., Ruzhansky, M. (eds) Progress in Partial Differential Equations. Springer Proceedings in Mathematics & Statistics, vol 44. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00125-8_10

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