A priori estimates to solutions of the time-fractional convection-diffusion-reaction equation coupled with the Darcy system

被引：8
|
作者：
Hendy, Ahmed S. [1 ]
Zaky, Mahmoud A. [2 ,3 ]
机构：
[1] Ural Fed Univ, Inst Nat Sci & Math, Dept Computat Math & Comp Sci, 19 Mira St, Ekaterinburg 620002, Russia
[2] Natl Res Ctr, Dept Appl Math, Cairo 12622, Egypt
[3] Nazarbayev Univ, Dept Math, Nur Sultan, Kazakhstan
来源：
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2022年 / 109卷
关键词：
Time fractional convection-diffusion; Darcy's law; A priori estimates; Existence and uniqueness; POROUS-MEDIA;
D O I：
10.1016/j.cnsns.2022.106288
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the Darcy flow equation coupled with the Caputo time-fractional convection-reaction-diffusion equations. This system describes the concentration distribution of a fluid running through a porous medium. A priori estimates are established for the solution by employing the method of energy inequalities. The existence, uniqueness and regularity properties of a weak solution are studied. Our analysis relies on two novel and different methodologies in combination with two alternative variational formulations. (C) 2022 Elsevier B.V. All rights reserved.
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页数：7
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