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Symmetry 2019, 11(1), 73; https://doi.org/10.3390/sym11010073

On a Generalization of the Initial-Boundary Problem for the Vibrating String Equation

1
Institute of Mathematics of Academy of Sciences of Uzbekistan, Tashkent 100125, Uzbekistan
2
Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia
3
Department of Electrical and Electronic Engineering, Istanbul Gelisim University, Avcilar, Istanbul 34310, Turkey
*
Author to whom correspondence should be addressed.
Received: 26 November 2018 / Revised: 26 December 2018 / Accepted: 7 January 2019 / Published: 10 January 2019
(This article belongs to the Special Issue Integral Transforms and Operational Calculus)
Full-Text   |   PDF [243 KB, uploaded 10 January 2019]

Abstract

In the present paper, we study a generalization of the initial-boundary problem for the inhomogeneous vibrating string equation. The initial conditions include the higher order derivatives of the unknown function. The problem is studied under homogeneous boundary conditions of the first kind. The uniqueness and existence of a regular solution of the problem are proved. To prove the main result we use the spectral decomposition method. View Full-Text
Keywords: vibrating string equation; initial conditions; spectral decomposition; regular solution; the uniqueness of the solution; the existence of a solution vibrating string equation; initial conditions; spectral decomposition; regular solution; the uniqueness of the solution; the existence of a solution
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Amanov, D.; Ibragimov, G.; Kılıçman, A. On a Generalization of the Initial-Boundary Problem for the Vibrating String Equation. Symmetry 2019, 11, 73.

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