On a boundary value problem for a third-order parabolic-hyperbolic type equation with a displacement boundary condition in its hyperbolicity domain
In the article, we investigate a boundary-value problem with a third-order inhomogeneous parabolic-hyperbolic equation with a wave operator in a hyperbolicity domain. A linear combination with variable coefficients in terms of derivatives of the sought function on independent characteristics, as we...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2020-07-01
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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/41987/28009 |
| _version_ | 1818142020447764480 |
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| author | Zhiraslan Anatolievich Balkizov |
| author_facet | Zhiraslan Anatolievich Balkizov |
| author_sort | Zhiraslan Anatolievich Balkizov |
| collection | DOAJ |
| description | In the article, we investigate a boundary-value problem with a third-order inhomogeneous parabolic-hyperbolic equation with a wave operator in a hyperbolicity domain. A linear combination with variable coefficients in terms of derivatives of the sought function on independent characteristics, as well as on the line of type and order changing is specified as a boundary condition. We have established necessary and sufficient conditions that guarantee existence and uniqueness of a regular solution to the problem under study. In some cases, a solution representation is written out explicitly. |
| first_indexed | 2024-12-11T11:09:08Z |
| format | Article |
| id | doaj.art-8112a06d245e4102a53e28ad5e9906b1 |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-12-11T11:09:08Z |
| publishDate | 2020-07-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-8112a06d245e4102a53e28ad5e9906b12022-12-22T01:09:36ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812020-07-0124221122510.14498/vsgtu169437973On a boundary value problem for a third-order parabolic-hyperbolic type equation with a displacement boundary condition in its hyperbolicity domainZhiraslan Anatolievich Balkizov0Institute of Applied Mathematics and AutomationIn the article, we investigate a boundary-value problem with a third-order inhomogeneous parabolic-hyperbolic equation with a wave operator in a hyperbolicity domain. A linear combination with variable coefficients in terms of derivatives of the sought function on independent characteristics, as well as on the line of type and order changing is specified as a boundary condition. We have established necessary and sufficient conditions that guarantee existence and uniqueness of a regular solution to the problem under study. In some cases, a solution representation is written out explicitly.https://journals.eco-vector.com/1991-8615/article/viewFile/41987/28009degenerate hyperbolic equationequation with multiple characteristicsparabolic-hyperbolic equation of third orderproblems with a shift |
| spellingShingle | Zhiraslan Anatolievich Balkizov On a boundary value problem for a third-order parabolic-hyperbolic type equation with a displacement boundary condition in its hyperbolicity domain Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki degenerate hyperbolic equation equation with multiple characteristics parabolic-hyperbolic equation of third order problems with a shift |
| title | On a boundary value problem for a third-order parabolic-hyperbolic type equation with a displacement boundary condition in its hyperbolicity domain |
| title_full | On a boundary value problem for a third-order parabolic-hyperbolic type equation with a displacement boundary condition in its hyperbolicity domain |
| title_fullStr | On a boundary value problem for a third-order parabolic-hyperbolic type equation with a displacement boundary condition in its hyperbolicity domain |
| title_full_unstemmed | On a boundary value problem for a third-order parabolic-hyperbolic type equation with a displacement boundary condition in its hyperbolicity domain |
| title_short | On a boundary value problem for a third-order parabolic-hyperbolic type equation with a displacement boundary condition in its hyperbolicity domain |
| title_sort | on a boundary value problem for a third order parabolic hyperbolic type equation with a displacement boundary condition in its hyperbolicity domain |
| topic | degenerate hyperbolic equation equation with multiple characteristics parabolic-hyperbolic equation of third order problems with a shift |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/41987/28009 |
| work_keys_str_mv | AT zhiraslananatolievichbalkizov onaboundaryvalueproblemforathirdorderparabolichyperbolictypeequationwithadisplacementboundaryconditioninitshyperbolicitydomain |