The problem with Saigo operators for a hyperbolic equation that degenerates inside the domain
A nonlocal problem is investigated for a degenerate hyperbolic equation $$ |y|^{m} u_{xx}-u_{yy}+a |y|^{\frac{m}{2}-1} u_{x}=0 $$ in a domain bounded by the characteristics of this equation. The boundary condition for this problem contains a linear combination of generalized fractional integro-diffe...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2017-09-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
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| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/20553/16800 |
| _version_ | 1818059803193245696 |
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| author | Oleg A Repin |
| author_facet | Oleg A Repin |
| author_sort | Oleg A Repin |
| collection | DOAJ |
| description | A nonlocal problem is investigated for a degenerate hyperbolic equation $$ |y|^{m} u_{xx}-u_{yy}+a |y|^{\frac{m}{2}-1} u_{x}=0 $$ in a domain bounded by the characteristics of this equation. The boundary condition for this problem contains a linear combination of generalized fractional integro-differentiation operators with a hypergeometric Gauss function in the kernel. The uniqueness of the solution is proved using the Tricomi method. The existence of a solution is equivalent to the solvability of a singular integral equation with a Cauchy kernel. |
| first_indexed | 2024-12-10T13:22:19Z |
| format | Article |
| id | doaj.art-c5e47fd870f54b81a72d2350e486e380 |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-12-10T13:22:19Z |
| publishDate | 2017-09-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-c5e47fd870f54b81a72d2350e486e3802022-12-22T01:47:17ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812017-09-0121347348010.14498/vsgtu155617973The problem with Saigo operators for a hyperbolic equation that degenerates inside the domainOleg A Repin0Samara State Economic UniversityA nonlocal problem is investigated for a degenerate hyperbolic equation $$ |y|^{m} u_{xx}-u_{yy}+a |y|^{\frac{m}{2}-1} u_{x}=0 $$ in a domain bounded by the characteristics of this equation. The boundary condition for this problem contains a linear combination of generalized fractional integro-differentiation operators with a hypergeometric Gauss function in the kernel. The uniqueness of the solution is proved using the Tricomi method. The existence of a solution is equivalent to the solvability of a singular integral equation with a Cauchy kernel.https://journals.eco-vector.com/1991-8615/article/viewFile/20553/16800boundary value problemfractional integro-differentiation operatorsgauss functionsingular integral equation |
| spellingShingle | Oleg A Repin The problem with Saigo operators for a hyperbolic equation that degenerates inside the domain Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki boundary value problem fractional integro-differentiation operators gauss function singular integral equation |
| title | The problem with Saigo operators for a hyperbolic equation that degenerates inside the domain |
| title_full | The problem with Saigo operators for a hyperbolic equation that degenerates inside the domain |
| title_fullStr | The problem with Saigo operators for a hyperbolic equation that degenerates inside the domain |
| title_full_unstemmed | The problem with Saigo operators for a hyperbolic equation that degenerates inside the domain |
| title_short | The problem with Saigo operators for a hyperbolic equation that degenerates inside the domain |
| title_sort | problem with saigo operators for a hyperbolic equation that degenerates inside the domain |
| topic | boundary value problem fractional integro-differentiation operators gauss function singular integral equation |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/20553/16800 |
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