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We consider an initial-boundary problem with dynamic boundary condition for a hyperbolic equation in a rectangle. Dynamic boundary condition represents a relation between values of derivatives with respect of spacial variables of a required solution and first-order derivatives with respect to time variable. 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 Sobolev spaces.

About the authors

V. A. Kirichek

Samara National Research University

Author for correspondence.
Russian Federation

L. S. Pulkina

Samara National Research University

Russian Federation


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Copyright (c) 2017 В. А. Киричек, Л. С. Пулькина

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