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NONLOCAL PROBLEM WITH DYNAMICAL BOUNDARY CONDITIONS FOR HYPERBOLIC EQUATION
- Authors: Dyuzheva A.V.1
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Affiliations:
- Samara National Research University
- Issue: Vol 23, No 3 (2017)
- Pages: 18-25
- Section: Articles
- URL: https://journals.ssau.ru/est/article/view/5497
- DOI: https://doi.org/10.18287/2541-7525-2017-23-3-18-25
- ID: 5497
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Abstract
In this article, we consider a boundary-value problem with nonlocal dynamical conditions for hyperbolic equation. A feature of such conditions is the presence of both first and second order derivatives with respect to time-variable. Furthermore, boundary conditions are nonlocal to the extent that their representation is a relation between values of the derivatives on different parts of the boundary. The problem under consideration arise when we study vibration of a bar with damping and point masses. The existence and uniqueness of a generalized solution are proved. The proof is based on apriori estimates and Galerkin procedure.
About the authors
A. V. Dyuzheva
Samara National Research University
Author for correspondence.
Email: morenov.sv@ssau.ru
Russian Federation
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