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

被引：7

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.

引用

页数：7

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