Kelvin-Voigt equations with memory: existence, uniqueness and regularity of solutions
In general, the study of inverse problems is realizable only in the case when the corresponding direct problems have the unique solution with some necessary properties such as continuity and regularity. In this paper, we study initial-boundary value problems for the system of 2D-3D nonlinear Kelvin...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2023-12-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Subjects: | |
| Online Access: | https://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/606 |
| _version_ | 1797372712673345536 |
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| author | Kh. Khompysh N.K. Nugymanova |
| author_facet | Kh. Khompysh N.K. Nugymanova |
| author_sort | Kh. Khompysh |
| collection | DOAJ |
| description |
In general, the study of inverse problems is realizable only in the case when the corresponding direct problems have the unique solution with some necessary properties such as continuity and regularity. In this paper, we study initial-boundary value problems for the system of 2D-3D nonlinear Kelvin-Voigt equations with memory, which describes a motion of an incompressible homogeneous non-Newtonian fluids with viscoelastic and relaxation properties. The investigation of these direct problems is related to the study of inverse problems for this system, which requires the continuity and regularity of solutions to these direct problems and their derivatives. The system, in addition to the initial condition, is supplemented with one of the boundary conditions: stick and slip boundary conditions. In both cases of these boundary conditions, the global in time existence and uniqueness of strong solutions to these initial-boundary value problems were proved. Moreover, under suitable assumptions on the data, the regularity of solutions and their derivatives were established.
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| first_indexed | 2024-03-08T18:39:46Z |
| format | Article |
| id | doaj.art-4b93673023764f9c8c042c68607df1ad |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:39:46Z |
| publishDate | 2023-12-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-4b93673023764f9c8c042c68607df1ad2023-12-29T09:21:04ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112023-12-01112410.31489/2023m4/66-78606Kelvin-Voigt equations with memory: existence, uniqueness and regularity of solutionsKh. KhompyshN.K. Nugymanova In general, the study of inverse problems is realizable only in the case when the corresponding direct problems have the unique solution with some necessary properties such as continuity and regularity. In this paper, we study initial-boundary value problems for the system of 2D-3D nonlinear Kelvin-Voigt equations with memory, which describes a motion of an incompressible homogeneous non-Newtonian fluids with viscoelastic and relaxation properties. The investigation of these direct problems is related to the study of inverse problems for this system, which requires the continuity and regularity of solutions to these direct problems and their derivatives. The system, in addition to the initial condition, is supplemented with one of the boundary conditions: stick and slip boundary conditions. In both cases of these boundary conditions, the global in time existence and uniqueness of strong solutions to these initial-boundary value problems were proved. Moreover, under suitable assumptions on the data, the regularity of solutions and their derivatives were established. https://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/606Kelvin-Voigt systemslip and stick boundary conditionsstrong solutionsglobal existence and uniquenesssmoothness |
| spellingShingle | Kh. Khompysh N.K. Nugymanova Kelvin-Voigt equations with memory: existence, uniqueness and regularity of solutions Қарағанды университетінің хабаршысы. Математика сериясы Kelvin-Voigt system slip and stick boundary conditions strong solutions global existence and uniqueness smoothness |
| title | Kelvin-Voigt equations with memory: existence, uniqueness and regularity of solutions |
| title_full | Kelvin-Voigt equations with memory: existence, uniqueness and regularity of solutions |
| title_fullStr | Kelvin-Voigt equations with memory: existence, uniqueness and regularity of solutions |
| title_full_unstemmed | Kelvin-Voigt equations with memory: existence, uniqueness and regularity of solutions |
| title_short | Kelvin-Voigt equations with memory: existence, uniqueness and regularity of solutions |
| title_sort | kelvin voigt equations with memory existence uniqueness and regularity of solutions |
| topic | Kelvin-Voigt system slip and stick boundary conditions strong solutions global existence and uniqueness smoothness |
| url | https://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/606 |
| work_keys_str_mv | AT khkhompysh kelvinvoigtequationswithmemoryexistenceuniquenessandregularityofsolutions AT nknugymanova kelvinvoigtequationswithmemoryexistenceuniquenessandregularityofsolutions |