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PROBLEM WITH DYNAMIC BOUNDARY CONDITIONS FOR A HYPERBOLIC EQUATION
- Authors: Kirichek V.A.1, Pulkina L.S.1
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Affiliations:
- Samara National Research University
- Issue: Vol 23, No 1 (2017)
- Pages: 21-27
- Section: Articles
- URL: https://journals.ssau.ru/est/article/view/5143
- DOI: https://doi.org/10.18287/2541-7525-2017-23-1-21-27
- ID: 5143
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Abstract
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.
Email: morenov@ssau.ru
Russian Federation
L. S. Pulkina
Samara National Research University
Email: morenov@ssau.ru
Russian Federation
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