Abstract
In terms of requirements imposed on the boundary function, we obtain a necessary and sufficient condition for the generalized solution of a mixed problem for the wave equation with zero initial conditions and with boundary conditions of the first kind to belong to the class L p .
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Il’in, V.A. and Kuleshov, A.A., Generalized Solutions of the Wave Equation in the Classes L p and W 1p for p ≥ 1, Dokl. Akad. Nauk, 2012, vol. 446, no. 4, pp. 374–377.
Il’in, V.A. and Kuleshov, A.A., Criterion for a Generalized Solution of the Mixed Problem for the Wave Equation to Belong to the Class L p for p ≥ 1, Dokl. Akad. Nauk, 2012, vol. 446, no. 6, pp. 612–614.
Il’in, V.A. and Kuleshov, A.A., On Some Properties of Generalized Solutions of the Wave Equation in the Classes L p and W 1p for p ≥ 1, Differ. Uravn., 2012, vol. 48, no. 11, pp. 1493–1500.
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Original Russian Text © V.A. Il’in, A.A. Kuleshov, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 12, pp. 1607–1611.
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Il’in, V.A., Kuleshov, A.A. Necessary and sufficient condition for the generalized solution of a mixed problem for the wave equation to belong to the class L p for p ≥ 1. Diff Equat 48, 1572–1576 (2012). https://doi.org/10.1134/S0012266112120038
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DOI: https://doi.org/10.1134/S0012266112120038