A solely time-dependent source reconstruction in a multiterm time-fractional order diffusion equation with non-smooth solutions
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
A solely time-dependent source reconstruction in a multiterm time-fractional order diffusion equation with non-smooth solutions
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| Автор |
Hendy, A. S.
Van, Bockstal, K. |
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| Тематика |
CONVERGENCE
GRADED MESHES INVERSE SOURCE PROBLEM MULTITERM FRACTIONAL DIFFUSION NON-UNIFORM ROTHE’S METHOD PRIOR ESTIMATES |
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| Описание |
An inverse source problem for non-smooth multiterm time Caputo fractional diffusion with fractional order designed as β0 < β1 < ⋯ < βM < 1 is the case of study in a bounded Lipschitz domain in ℝd. The missing solely time-dependent source function is reconstructed from an additional integral measurement. The existence, uniqueness and regularity of a weak solution for the inverse source problem is investigated. We design a numerical algorithm based on Rothe’s method over graded meshes, derive a priori estimates and prove convergence of iterates towards the exact solution. An essential feature of the multiterm time Caputo fractional subdiffusion problem is that the solution possibly lacks the smoothness near the initial time, although it would be smooth away from t = 0. In this contribution, we will establish an extension of Grönwall’s inequalities for multiterm fractional operators. This extension will be crucial for showing the existence of a unique solution to the inverse problem. The theoretical obtained results are supported by some numerical experiments. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Research Foundation - Flanders, (106016/12P2919N) Fonds Wetenschappelijk Onderzoek, FWO K. Van Bockstal is supported by a postdoctoral fellowship of the Research Foundation - Flanders (106016/12P2919N). |
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| Дата |
2024-04-08T11:06:54Z
2024-04-08T11:06:54Z 2022 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) Published version (info:eu-repo/semantics/publishedVersion) |
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| Идентификатор |
Hendy, AS & Van Bockstal, K 2022, 'A solely time-dependent source reconstruction in a multiterm time-fractional order diffusion equation with non-smooth solutions', Numerical Algorithms, Том. 90, № 2, стр. 809-832. https://doi.org/10.1007/s11075-021-01210-w
Hendy, A. S., & Van Bockstal, K. (2022). A solely time-dependent source reconstruction in a multiterm time-fractional order diffusion equation with non-smooth solutions. Numerical Algorithms, 90(2), 809-832. https://doi.org/10.1007/s11075-021-01210-w 1017-1398 Final All Open Access; Green Open Access https://biblio.ugent.be/publication/8747792/file/8747805.pdf https://biblio.ugent.be/publication/8747792/file/8747805.pdf http://elar.urfu.ru/handle/10995/131364 10.1007/s11075-021-01210-w 85117946648 000710835800001 |
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| Язык |
en
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| Права |
Open access (info:eu-repo/semantics/openAccess)
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| Формат |
application/pdf
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| Издатель |
Springer
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| Источник |
Numerical Algorithms
Numerical Algorithms |
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