A generalization of the Darcy-Forchheimer equation involving an implicit, pressure-dependent relation between the drag force and the velocity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:424

Article

Bulicek, Miroslav¹  Malek, Josef¹  Zabensky, Josef¹ 

[1] Charles Univ Prague, Fac Math & Phys, Math Inst, Prague 18675 8, Czech Republic

关键词: Darcy-Forchheimer equation;    Pressure dependent material coefficient;    Implicit constitutive theory;    Maximal monotone graph;    Existence theory;    Maximum/minimum principle;   

DOI  :  10.1016/j.jmaa.2014.11.053

来源: Elsevier

【 摘 要 】

We study mathematical properties of steady flows described by the system of equations generalizing the classical porous media models of Darcy and Forchheimer. The considered generalizations are outlined by implicit relations between the drag force and the velocity, that are in addition parametrized by the pressure. We analyze such drag force-velocity relations which are described through a maximal monotone graph varying continuously with the pressure. Large-data existence of a solution to this system is established, whereupon we show that under certain assumptions on data, the pressure satisfies a maximum or minimum principle, even if the drag coefficient depends on the pressure exponentially. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free