Abstract
This paper provides a modified method that allows one to solve the problem of the optimal boundary controls μ(t) and ν(t) of displacements at two ends of a string for a large time interval T = 2ln, where n = 1, 2, 3, … It should be noted that the minimization was made in the space L p with p ≥ 1. Besides, it was found that the derivatives of above-mentioned functions are 2l-periodic functions.
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References
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The work was supported by the grant MK − 3400. 2017. 1.
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Smirnov, I., Dmitrieva, A. (2017). Minimization of the L p -Norm, p ≥ 1 of Dirichlet-Type Boundary Controls for the 1D Wave Equation. In: Takáč, M., Terlaky, T. (eds) Modeling and Optimization: Theory and Applications. MOPTA 2016. Springer Proceedings in Mathematics & Statistics, vol 213. Springer, Cham. https://doi.org/10.1007/978-3-319-66616-7_6
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DOI: https://doi.org/10.1007/978-3-319-66616-7_6
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