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A problem with a nonlocal, with respect to time, condition for multidimensional hyperbolic equations

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Abstract

We study a boundary-value problem for a hyperbolic equation with a nonlocal with respect to time-variable integral condition. We obtain sufficient conditions for unique solvability of the nonlocal problem. The proof is based on reduction of the nonlocal first-type condition to the second-type one. This allows to reduce the nonlocal problem to an operator equation. We show that unique solvability of the operator equation implies the existence of a unique solution to the problem.

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Correspondence to L. S. Pul’kina.

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Original Russian Text © L.S. Pul’kina, A.E. Savenkova, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 10, pp. 41–52.

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Pul’kina, L.S., Savenkova, A.E. A problem with a nonlocal, with respect to time, condition for multidimensional hyperbolic equations. Russ Math. 60, 33–43 (2016). https://doi.org/10.3103/S1066369X16100066

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  • DOI: https://doi.org/10.3103/S1066369X16100066

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