Homogenized Models with Memory Effect for Heterogeneous Periodic Media
The homogenization of initial boundary value problems for heat conduction equations with asymptotically degenerate rapidly oscillating periodic coefficients are considered. Such problems model thermal processes in heterogeneous periodic media. Homogenized problems (whose solutions determine approxim...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Oles Honchar Dnipro National University
2022-08-01
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| Series: | Journal of Optimization, Differential Equations and Their Applications |
| Subjects: | |
| Online Access: | https://model-dnu.dp.ua/index.php/SM/article/view/171 |
| _version_ | 1797953575057358848 |
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| author | Gennadiy V. Sandrakov Vladimir V. Semenov |
| author_facet | Gennadiy V. Sandrakov Vladimir V. Semenov |
| author_sort | Gennadiy V. Sandrakov |
| collection | DOAJ |
| description | The homogenization of initial boundary value problems for heat conduction equations with asymptotically degenerate rapidly oscillating periodic coefficients are considered. Such problems model thermal processes in heterogeneous periodic media. Homogenized problems (whose solutions determine approximate asymptotics for solutions of the original problems) are presented. Estimates for the accuracy of the asymptotics and relevant convergence theorem are discussed. The homogenized problems have the form of initial boundary value problems for integro-differential equations in convolutions. The presence of convolutions in models for media is called the memory effect. Statements about the solvability and regularity for the problems and the homogenized problems are proved. These results are optimal even in the case of zero convolutions, when the homogenized problems coincide with the classical heat conduction problems. |
| first_indexed | 2024-04-10T23:04:13Z |
| format | Article |
| id | doaj.art-1afae4d733114e5995f3a54efef26ad2 |
| institution | Directory Open Access Journal |
| issn | 2617-0108 2663-6824 |
| language | English |
| last_indexed | 2024-04-10T23:04:13Z |
| publishDate | 2022-08-01 |
| publisher | Oles Honchar Dnipro National University |
| record_format | Article |
| series | Journal of Optimization, Differential Equations and Their Applications |
| spelling | doaj.art-1afae4d733114e5995f3a54efef26ad22023-01-13T12:20:59ZengOles Honchar Dnipro National UniversityJournal of Optimization, Differential Equations and Their Applications2617-01082663-68242022-08-0130211810.15421/142206163Homogenized Models with Memory Effect for Heterogeneous Periodic MediaGennadiy V. Sandrakov0Vladimir V. Semenov1Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of KyivFaculty of Computer Science and Cybernetics, Taras Shevchenko National University of KyivThe homogenization of initial boundary value problems for heat conduction equations with asymptotically degenerate rapidly oscillating periodic coefficients are considered. Such problems model thermal processes in heterogeneous periodic media. Homogenized problems (whose solutions determine approximate asymptotics for solutions of the original problems) are presented. Estimates for the accuracy of the asymptotics and relevant convergence theorem are discussed. The homogenized problems have the form of initial boundary value problems for integro-differential equations in convolutions. The presence of convolutions in models for media is called the memory effect. Statements about the solvability and regularity for the problems and the homogenized problems are proved. These results are optimal even in the case of zero convolutions, when the homogenized problems coincide with the classical heat conduction problems.https://model-dnu.dp.ua/index.php/SM/article/view/171heat conduction equationsapproximate asymptoticssolvability result |
| spellingShingle | Gennadiy V. Sandrakov Vladimir V. Semenov Homogenized Models with Memory Effect for Heterogeneous Periodic Media Journal of Optimization, Differential Equations and Their Applications heat conduction equations approximate asymptotics solvability result |
| title | Homogenized Models with Memory Effect for Heterogeneous Periodic Media |
| title_full | Homogenized Models with Memory Effect for Heterogeneous Periodic Media |
| title_fullStr | Homogenized Models with Memory Effect for Heterogeneous Periodic Media |
| title_full_unstemmed | Homogenized Models with Memory Effect for Heterogeneous Periodic Media |
| title_short | Homogenized Models with Memory Effect for Heterogeneous Periodic Media |
| title_sort | homogenized models with memory effect for heterogeneous periodic media |
| topic | heat conduction equations approximate asymptotics solvability result |
| url | https://model-dnu.dp.ua/index.php/SM/article/view/171 |
| work_keys_str_mv | AT gennadiyvsandrakov homogenizedmodelswithmemoryeffectforheterogeneousperiodicmedia AT vladimirvsemenov homogenizedmodelswithmemoryeffectforheterogeneousperiodicmedia |