On the problem for the mixed-type degenerate equation with Caputo and Erdelyi – Kober operators of fractional order
UDC 517.9 We establish the existence and uniqueness of the solution of a local problem for the degenerate parabolic-hyperbolic-type equations with loaded terms containing the trace of solution in the Erdelyi – Kober integrals. Since, the trace of solution (i.e., $u(x, 0)$) appears in the Erdelyi –...
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| Datum: | 2019 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2019
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1471 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.9
We establish the existence and uniqueness of the solution of a local problem for the degenerate parabolic-hyperbolic-type
equations with loaded terms containing the trace of solution in the Erdelyi – Kober integrals. Since, the trace of solution
(i.e., $u(x, 0)$) appears in the Erdelyi – Kober integrals and the hyperbolic-type equation is degenerated in the line $y = 0$,
we use some properties and estimates for hypergeometric functions and, in addition, some integral equalities in proving the
existence and uniqueness of solution of the investigated problem. |
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