On Some Non-local Boundary Value and Internal Boundary Value Problems for the String Oscillation Equation
The work is devoted to the problem of setting new boundary and internal boundary value problems for hyperbolic equations. The consideration of these settings is given on the example of a wave equation. The research involves the d’Alembert method, the mean value theorem and the method of successive...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Academician Ye.A. Buketov Karaganda University
2023-06-01
|
| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Subjects: | |
| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/564 |
| _version_ | 1797371253307211776 |
|---|---|
| author | A.Kh. Attaev |
| author_facet | A.Kh. Attaev |
| author_sort | A.Kh. Attaev |
| collection | DOAJ |
| description |
The work is devoted to the problem of setting new boundary and internal boundary value problems for hyperbolic equations. The consideration of these settings is given on the example of a wave equation. The research involves the d’Alembert method, the mean value theorem and the method of successive approximations. The paper formulates and studies a number of non-local problems summarizing the classical Goursat and Dardu tasks. Some of them are marginal, and the other part is internal-marginal, and in both cases both characteristic and uncharacteristic displacements are considered. It should also be noted that a number of problems discussed below arose as a special case in the construction of the theory of correct problems for the model loaded equation of string oscillation.
|
| first_indexed | 2024-03-08T18:17:14Z |
| format | Article |
| id | doaj.art-03a460d3445f42e39a30b9bb4e3ccde2 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:17:14Z |
| publishDate | 2023-06-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-03a460d3445f42e39a30b9bb4e3ccde22023-12-31T10:28:16ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112023-06-01110210.31489/2023m2/35-44On Some Non-local Boundary Value and Internal Boundary Value Problems for the String Oscillation EquationA.Kh. Attaev The work is devoted to the problem of setting new boundary and internal boundary value problems for hyperbolic equations. The consideration of these settings is given on the example of a wave equation. The research involves the d’Alembert method, the mean value theorem and the method of successive approximations. The paper formulates and studies a number of non-local problems summarizing the classical Goursat and Dardu tasks. Some of them are marginal, and the other part is internal-marginal, and in both cases both characteristic and uncharacteristic displacements are considered. It should also be noted that a number of problems discussed below arose as a special case in the construction of the theory of correct problems for the model loaded equation of string oscillation. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/564Wave equationgeneral solutionCauchy problemGoursat problemDarboux problemproblem with characteristic shift |
| spellingShingle | A.Kh. Attaev On Some Non-local Boundary Value and Internal Boundary Value Problems for the String Oscillation Equation Қарағанды университетінің хабаршысы. Математика сериясы Wave equation general solution Cauchy problem Goursat problem Darboux problem problem with characteristic shift |
| title | On Some Non-local Boundary Value and Internal Boundary Value Problems for the String Oscillation Equation |
| title_full | On Some Non-local Boundary Value and Internal Boundary Value Problems for the String Oscillation Equation |
| title_fullStr | On Some Non-local Boundary Value and Internal Boundary Value Problems for the String Oscillation Equation |
| title_full_unstemmed | On Some Non-local Boundary Value and Internal Boundary Value Problems for the String Oscillation Equation |
| title_short | On Some Non-local Boundary Value and Internal Boundary Value Problems for the String Oscillation Equation |
| title_sort | on some non local boundary value and internal boundary value problems for the string oscillation equation |
| topic | Wave equation general solution Cauchy problem Goursat problem Darboux problem problem with characteristic shift |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/564 |
| work_keys_str_mv | AT akhattaev onsomenonlocalboundaryvalueandinternalboundaryvalueproblemsforthestringoscillationequation |