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

Abstract

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.

Keywords

• Structural stability
• Forchheimer equations
• Darcy equations
• Interface boundary condition