Method of functional parametrization for solving a semi-periodic initial problem for fourth-order partial differential equations
A semi-periodic initial boundary-value problem for a fourth-order system of partial differential equations is considered. Using the method of functional parametrization, an additional parameter is carried out and the studied problem is reduced to the equivalent semi-periodic problem for a system of...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2020-12-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
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| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/373 |
| _version_ | 1797372634675019776 |
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| author | A.T. Assanova Zh.S. Tokmurzin |
| author_facet | A.T. Assanova Zh.S. Tokmurzin |
| author_sort | A.T. Assanova |
| collection | DOAJ |
| description |
A semi-periodic initial boundary-value problem for a fourth-order system of partial differential equations is considered. Using the method of functional parametrization, an additional parameter is carried out and the studied problem is reduced to the equivalent semi-periodic problem for a system of integro-differential equations of hyperbolic type second order with functional parameters and integral relations. An interrelation between the semi-periodic problem for the system of integro-differential equations of hyperbolic type and a family of Cauchy problems for a system of ordinary differential equations is established. Algorithms for finding of solutions to an equivalent problem are constructed and their convergence is proved. Sufficient conditions of a unique solvability to the semi-periodic initial boundary value problem for the fourth order system of partial differential equations are obtained.
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| first_indexed | 2024-03-08T18:38:40Z |
| format | Article |
| id | doaj.art-19c2217dadd8464caefb0d94dadded31 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:38:40Z |
| publishDate | 2020-12-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-19c2217dadd8464caefb0d94dadded312023-12-29T10:20:12ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112020-12-01100410.31489/2020m4/5-16Method of functional parametrization for solving a semi-periodic initial problem for fourth-order partial differential equationsA.T. AssanovaZh.S. Tokmurzin A semi-periodic initial boundary-value problem for a fourth-order system of partial differential equations is considered. Using the method of functional parametrization, an additional parameter is carried out and the studied problem is reduced to the equivalent semi-periodic problem for a system of integro-differential equations of hyperbolic type second order with functional parameters and integral relations. An interrelation between the semi-periodic problem for the system of integro-differential equations of hyperbolic type and a family of Cauchy problems for a system of ordinary differential equations is established. Algorithms for finding of solutions to an equivalent problem are constructed and their convergence is proved. Sufficient conditions of a unique solvability to the semi-periodic initial boundary value problem for the fourth order system of partial differential equations are obtained. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/373semi-periodic initial boundary-value problemfourth-order system of partial differential equationsthe method of functional parametrizationsemi-periodic problemsystem of integro-differential equations of hyperbolic type second orderfamily of Cauchy problems |
| spellingShingle | A.T. Assanova Zh.S. Tokmurzin Method of functional parametrization for solving a semi-periodic initial problem for fourth-order partial differential equations Қарағанды университетінің хабаршысы. Математика сериясы semi-periodic initial boundary-value problem fourth-order system of partial differential equations the method of functional parametrization semi-periodic problem system of integro-differential equations of hyperbolic type second order family of Cauchy problems |
| title | Method of functional parametrization for solving a semi-periodic initial problem for fourth-order partial differential equations |
| title_full | Method of functional parametrization for solving a semi-periodic initial problem for fourth-order partial differential equations |
| title_fullStr | Method of functional parametrization for solving a semi-periodic initial problem for fourth-order partial differential equations |
| title_full_unstemmed | Method of functional parametrization for solving a semi-periodic initial problem for fourth-order partial differential equations |
| title_short | Method of functional parametrization for solving a semi-periodic initial problem for fourth-order partial differential equations |
| title_sort | method of functional parametrization for solving a semi periodic initial problem for fourth order partial differential equations |
| topic | semi-periodic initial boundary-value problem fourth-order system of partial differential equations the method of functional parametrization semi-periodic problem system of integro-differential equations of hyperbolic type second order family of Cauchy problems |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/373 |
| work_keys_str_mv | AT atassanova methodoffunctionalparametrizationforsolvingasemiperiodicinitialproblemforfourthorderpartialdifferentialequations AT zhstokmurzin methodoffunctionalparametrizationforsolvingasemiperiodicinitialproblemforfourthorderpartialdifferentialequations |