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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-01-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/11/1/73 |
| _version_ | 1811187659096195072 |
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| author | Djumaklich Amanov Gafurjan Ibragimov Adem Kılıçman |
| author_facet | Djumaklich Amanov Gafurjan Ibragimov Adem Kılıçman |
| author_sort | Djumaklich Amanov |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T14:05:57Z |
| format | Article |
| id | doaj.art-8303b83d92644fb2a093a3d16dbb1518 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T14:05:57Z |
| publishDate | 2019-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-8303b83d92644fb2a093a3d16dbb15182022-12-22T04:19:53ZengMDPI AGSymmetry2073-89942019-01-011117310.3390/sym11010073sym11010073On a Generalization of the Initial-Boundary Problem for the Vibrating String EquationDjumaklich Amanov0Gafurjan Ibragimov1Adem Kılıçman2Institute of Mathematics of Academy of Sciences of Uzbekistan, Tashkent 100125, UzbekistanDepartment of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Selangor, MalaysiaDepartment of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Selangor, MalaysiaIn 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.http://www.mdpi.com/2073-8994/11/1/73vibrating string equationinitial conditionsspectral decompositionregular solutionthe uniqueness of the solutionthe existence of a solution |
| spellingShingle | Djumaklich Amanov Gafurjan Ibragimov Adem Kılıçman On a Generalization of the Initial-Boundary Problem for the Vibrating String Equation Symmetry vibrating string equation initial conditions spectral decomposition regular solution the uniqueness of the solution the existence of a solution |
| title | On a Generalization of the Initial-Boundary Problem for the Vibrating String Equation |
| title_full | On a Generalization of the Initial-Boundary Problem for the Vibrating String Equation |
| title_fullStr | On a Generalization of the Initial-Boundary Problem for the Vibrating String Equation |
| title_full_unstemmed | On a Generalization of the Initial-Boundary Problem for the Vibrating String Equation |
| title_short | On a Generalization of the Initial-Boundary Problem for the Vibrating String Equation |
| title_sort | on a generalization of the initial boundary problem for the vibrating string equation |
| topic | vibrating string equation initial conditions spectral decomposition regular solution the uniqueness of the solution the existence of a solution |
| url | http://www.mdpi.com/2073-8994/11/1/73 |
| work_keys_str_mv | AT djumaklichamanov onageneralizationoftheinitialboundaryproblemforthevibratingstringequation AT gafurjanibragimov onageneralizationoftheinitialboundaryproblemforthevibratingstringequation AT ademkılıcman onageneralizationoftheinitialboundaryproblemforthevibratingstringequation |