Structural stability for the Forchheimer equations interfacing with a Darcy fluid in a bounded region in R 3 $\mathbb{R}^{3}$

Boundary Value Problems

Yan Liu¹  Jincheng Shi² 

[1] Department of Applied Mathematics, Guangdong University of Finance;Department of Mathematics, Guangzhou Huashang College;

关键词: Structural stability;    Forchheimer equations;    Darcy equations;    Interface boundary condition;   

DOI  :  10.1186/s13661-021-01525-6

来源: DOAJ

【 摘 要 】

Abstract The structural stability for the Forchheimer fluid interfacing with a Darcy fluid in a bounded region in R 3 $\mathbb{R}^{3}$ was studied. We assumed that the nonlinear fluid was governed by the Forchheimer equations in Ω 1 $\Omega _{1}$ , while in Ω 2 $\Omega _{2}$ , we supposed that the flow satisfies the Darcy equations. With the aid of some useful a priori bounds, we were able to demonstrate the continuous dependence results for the Forchheimer coefficient λ.

【 授权许可】

Unknown