Abstract
The present paper deals with finding an optimal control of vibrations of a spherical layer, where the control is given by conditions of the third kind on the boundary. We continue and develop the results obtained by V.A. Il’in, E.I. Moiseev, and their students. We consider a more general control optimality criterion than in the previous papers.
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Sergeev, S.A., A Remark on the Problem of the Optimal Boundary Control of Vibrations of a Spherical Layer, Differ. Uravn., 2009, vol. 45, no. 10, pp. 1480–1491.
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Il’in, V.A. and Moiseev, E.I., Minimization of the L p-Norm for p ≥ 1 of the Derivative of a Boundary Displacement Control on an Arbitrary Sufficiently Large Time Interval [0, T], Differ. Uravn., 2006, vol. 42, no. 11, pp. 1558–1570.
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Original Russian Text © S.A. Sergeev, 2010, published in Differentsial’nye Uravneniya, 2010, Vol. 46, No. 1, pp. 129–138.
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Sergeev, S.A. On the problem of optimal boundary control of vibrations of a spherical layer by a special third boundary condition. Diff Equat 46, 132–141 (2010). https://doi.org/10.1134/S0012266110010143
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DOI: https://doi.org/10.1134/S0012266110010143