Просмотреть запись

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
 
Автор Van, Bockstal, K.
Zaky, M. A.
Hendy, A. S.
 
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
 
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) .
 
Дата 2024-04-08T11:08:02Z
2024-04-08T11:08:02Z
2022
 
Тип Article
Journal article (info:eu-repo/semantics/article)
Published version (info:eu-repo/semantics/publishedVersion)
 
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
 
Язык en
 
Связанные ресурсы info:eu-repo/grantAgreement/RSF//22-21-00075
 
Права Open access (info:eu-repo/semantics/openAccess)
 
Формат application/pdf
 
Издатель Elsevier B.V.
 
Источник Communications in Nonlinear Science and Numerical Simulation
Communications in Nonlinear Science and Numerical Simulation