On the existence and uniqueness of solutions to a nonlinear variable order time-fractional reaction–diffusion equation with delay
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
On the existence and uniqueness of solutions to a nonlinear variable order time-fractional reaction–diffusion equation with delay
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| Автор |
Van, Bockstal, K.
Zaky, M. A. Hendy, A. S. |
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| Тематика |
A PRIORI ESTIMATES
EXISTENCE ROTHE'S METHOD TIME DELAY UNIQUENESS VARIABLE ORDER SUBDIFFUSION NONLINEAR EQUATIONS PARTIAL DIFFERENTIAL EQUATIONS TIMING CIRCUITS A-PRIORI ESTIMATES EXISTENCE EXISTENCE AND UNIQUENESS OF SOLUTION ROTHE METHOD SUBDIFFUSION TIME-DELAYS UNIQUENESS VARIABLE ORDER SUBDIFFUSION VARIABLES ORDERING WEAK SOLUTION TIME DELAY |
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| Описание |
In this article, our purpose is to study the existence and uniqueness of a solution to a damped variable order fractional subdiffusion equation with time delay. Under weak assumptions on the data, we prove the uniqueness of a weak solution to the problem under consideration. The method of semi-discretization is extended to this kind of time fractional parabolic problem with delay in the case that the time delay parameter s>0 satisfies s⩽T, where T denotes the final time. As a consequence, two a priori estimates are predicted based on a discrete variational formulation of the problem. The existence of the problem's weak solution on the time frame 0,⌊[Formula presented]⌋s is established by the aid of these derived a priori estimates. The paper is closed by introducing a fully discrete scheme based on Galerkin Legendre spectral approximation for the spatial operator and the backward Euler difference approximation for the temporal variable order operator. Accordingly, the accuracy and efficiency of the proposed scheme are justified by giving some numerical experiments for the sake of clearness. © 2022 Elsevier B.V.
National Research Centre, NRC Fonds Wetenschappelijk Onderzoek, FWO, (106016/12P2919N) Russian Science Foundation, RSF, (22-21-00075) K. Van Bockstal is supported by a postdoctoral fellowship of the Research Foundation - Flanders ( 106016/12P2919N ). Ahmed S. Hendy wishes to acknowledge the support of the RSF grant, project 22-21-00075 . Mahmoud A. Zaky wishes to acknowledge the support of the National Research Centre of Egypt (NRC) . |
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| Дата |
2024-04-08T11:08:02Z
2024-04-08T11:08:02Z 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 |
Van Bockstal, K, Zaky, MA & Hendy, AS 2022, 'On the existence and uniqueness of solutions to a nonlinear variable order time-fractional reaction–diffusion equation with delay', Communications in Nonlinear Science and Numerical Simulation, Том. 115, 106755. https://doi.org/10.1016/j.cnsns.2022.106755
Van Bockstal, K., Zaky, M. A., & Hendy, A. S. (2022). On the existence and uniqueness of solutions to a nonlinear variable order time-fractional reaction–diffusion equation with delay. Communications in Nonlinear Science and Numerical Simulation, 115, [106755]. https://doi.org/10.1016/j.cnsns.2022.106755 1007-5704 Final All Open Access; Green Open Access https://biblio.ugent.be/publication/01GP0MQH7NMN6BF1442ECXGYPE/file/01GP0N4341T6WF2Q2EZXPS89FJ.pdf https://biblio.ugent.be/publication/01GP0MQH7NMN6BF1442ECXGYPE/file/01GP0N4341T6WF2Q2EZXPS89FJ.pdf http://elar.urfu.ru/handle/10995/131562 10.1016/j.cnsns.2022.106755 85135904895 000848354500007 |
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| Язык |
en
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| Связанные ресурсы |
info:eu-repo/grantAgreement/RSF//22-21-00075
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| Права |
Open access (info:eu-repo/semantics/openAccess)
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| Формат |
application/pdf
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| Издатель |
Elsevier B.V.
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| Источник |
Communications in Nonlinear Science and Numerical Simulation
Communications in Nonlinear Science and Numerical Simulation |
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