Solvability of a nonlocal problem for a hyperbolic equation with integral conditions
We study a nonlocal problem with integral conditions for a hyperbolic equation two independent variables. By introducing additional functional parameters, we investigated the solvability and construction of approximate solutions. The original problem is reduced to an equivalent problem consisting...
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| Format: | Article |
| Language: | English |
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Texas State University
2017-07-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2017/170/abstr.html |
| _version_ | 1831768896394231808 |
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| author | Anar T. Assanova |
| author_facet | Anar T. Assanova |
| author_sort | Anar T. Assanova |
| collection | DOAJ |
| description | We study a nonlocal problem with integral conditions for a hyperbolic equation
two independent variables. By introducing additional functional parameters,
we investigated the solvability and construction of approximate solutions.
The original problem is reduced to an equivalent problem consisting of
the Goursat problems for a hyperbolic equation with parameters and the
boundary value problem with integral condition for the ordinary differential
equations with respect to the parameters. Based on the algorithms for finding
solutions to the equivalent problem, we propose algorithms for finding
the approximate solutions, and prove their convergence.
Coefficient criteria for the unique solvability of nonlocal problem with
integral conditions for hyperbolic equation with mixed derivative are
also established. |
| first_indexed | 2024-12-22T07:09:41Z |
| format | Article |
| id | doaj.art-71dbb6651abe479bac1e614f6bdbedab |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-22T07:09:41Z |
| publishDate | 2017-07-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-71dbb6651abe479bac1e614f6bdbedab2022-12-21T18:34:33ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912017-07-012017170,112Solvability of a nonlocal problem for a hyperbolic equation with integral conditionsAnar T. Assanova0 Institute of Math., Almaty, Kazakhstan We study a nonlocal problem with integral conditions for a hyperbolic equation two independent variables. By introducing additional functional parameters, we investigated the solvability and construction of approximate solutions. The original problem is reduced to an equivalent problem consisting of the Goursat problems for a hyperbolic equation with parameters and the boundary value problem with integral condition for the ordinary differential equations with respect to the parameters. Based on the algorithms for finding solutions to the equivalent problem, we propose algorithms for finding the approximate solutions, and prove their convergence. Coefficient criteria for the unique solvability of nonlocal problem with integral conditions for hyperbolic equation with mixed derivative are also established.http://ejde.math.txstate.edu/Volumes/2017/170/abstr.htmlHyperbolic equationnonlocal problemintegral conditionalgorithmapproximate solution |
| spellingShingle | Anar T. Assanova Solvability of a nonlocal problem for a hyperbolic equation with integral conditions Electronic Journal of Differential Equations Hyperbolic equation nonlocal problem integral condition algorithm approximate solution |
| title | Solvability of a nonlocal problem for a hyperbolic equation with integral conditions |
| title_full | Solvability of a nonlocal problem for a hyperbolic equation with integral conditions |
| title_fullStr | Solvability of a nonlocal problem for a hyperbolic equation with integral conditions |
| title_full_unstemmed | Solvability of a nonlocal problem for a hyperbolic equation with integral conditions |
| title_short | Solvability of a nonlocal problem for a hyperbolic equation with integral conditions |
| title_sort | solvability of a nonlocal problem for a hyperbolic equation with integral conditions |
| topic | Hyperbolic equation nonlocal problem integral condition algorithm approximate solution |
| url | http://ejde.math.txstate.edu/Volumes/2017/170/abstr.html |
| work_keys_str_mv | AT anartassanova solvabilityofanonlocalproblemforahyperbolicequationwithintegralconditions |