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

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

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 un...

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Bibliographic Details
Main Authors: Djumaklich Amanov, Gafurjan Ibragimov, Adem Kılıçman
Format: Article
Language:English
Published: MDPI AG 2019-01-01
Series:Symmetry
Subjects:
vibrating string equation
initial conditions
spectral decomposition
regular solution
the uniqueness of the solution
the existence of a solution
Online Access:http://www.mdpi.com/2073-8994/11/1/73
Description
Summary: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.
ISSN:2073-8994

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