Abstract
The initial-boundary value problem for the wave equation is considered in the three-dimensional half-space. The oscillation process is initiated by the initial data and the boundary mode. We prove a theorem of existence and uniqueness of the solution; it is presented in the form of the generalized Kirchhoff formula. This work can be considered as a generalization to the three-dimensional case of the classical result for equations of oscillations of a semi-bounded string.
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Funding
The work is fulfilled under the financial support of the Program of the Presidium of the Russian Academy of Science (project no. 0314-2015-001013-01-275).
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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 6, pp. 3–10.
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Anikonov, D.S., Konovalova, D.S. Formula of Kirchhoff Type for Mixed Problem. Russ Math. 65, 1–7 (2021). https://doi.org/10.3103/S1066369X21060013
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DOI: https://doi.org/10.3103/S1066369X21060013