Abstract
We consider an initial-boundary problem with dynamic nonlocal boundary condition for a pseudohyperbolic fourth-order equation in a cylinder. Dynamic nonlocal boundary condition represents a relation between values of a required solution, its derivatives with respect to spatial variables, second-order derivatives with respect to time variable and an integral term. The main result lies in substantiation of solvability of this problem. We prove the existence and uniqueness of a generalized solution. The proof is based on the a priori estimates obtained in this paper, Galyorkin’s procedure and the properties of the Sobolev spaces.
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Original Russian Text © L.S. Pul’kina, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 9, pp. 42–50.
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Pul’kina, L.S. A problem with dynamic nonlocal condition for pseudohyperbolic equation. Russ Math. 60, 38–45 (2016). https://doi.org/10.3103/S1066369X16090048
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DOI: https://doi.org/10.3103/S1066369X16090048