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Closed-form expression for a generalized solution in W 1 p of a mixed problem describing radially symmetric vibrations of a three-dimensional ball

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Abstract

For any p ≥ 1 and any time interval [0, T], we derive a closed-form expression for a generalized solution in W 1 p of a mixed problem describing the radially symmetric vibrations of a three-dimensional ball with arbitrary initial conditions and an arbitrary boundary control on the ball surface by a boundary condition of the first kind.

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References

  1. Il’in, V.A., Boundary Control of Spherically Symmetric Vibrations of a Three-Dimensional Ball, Tr. Mat. Inst. Steklova, 2001, vol. 232, pp. 144–155.

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  2. Il’in, V.A., Boundary Control of Vibrations on Two Ends in Terms of a Generalized Solution of the Wave Equation with Finite Energy, Differ. Uravn., 2000, vol. 36, no. 11, pp. 1513–1528.

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  3. Il’in, V.A., Boundary Control of Vibrations at One End and the Other End Fixed in Terms of a Generalized Solution of the Wave Equation with Finite Energy, Differ. Uravn., 2000, vol. 36, no. 12, pp. 1670–1686.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    A. V. Kurkina

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  1. A. V. Kurkina
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Correspondence to A. V. Kurkina.

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Original Russian Text © A.V. Kurkina, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 1, pp. 48–54.

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Kurkina, A.V. Closed-form expression for a generalized solution in W 1 p of a mixed problem describing radially symmetric vibrations of a three-dimensional ball. Diff Equat 51, 47–53 (2015). https://doi.org/10.1134/S001226611501005X

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  • DOI: https://doi.org/10.1134/S001226611501005X

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