The incompressible limit of nonlinear diffusion equations porous medium type has attracted a lot attention in recent years, due to its ability link the weak formulation cell-population models free boundary problems Hele-Shaw type. Although vast literature is available on this singular limit, little known convergence rate solutions. In work, we compute negative Sobolev norm and, upon interpolati...

In order to handle the flow of a viscous incompressible fluid in a porous medium with cracks, the thickness of which cannot be neglected, we consider a model which couples the Darcy equations in the medium with the Stokes equations in the cracks by a new boundary condition at the interface, namely the continuity of the pressure. We prove that this model admits a unique solution and propose a mi...

Numerical study of the slip effects and radiative heat transfer on a steady state fully developed Williamson flow of an incompressible Newtonian fluid; between parallel vertical walls of a microchannel with isothermal walls in a porous medium is performed. The slip effects are considered at both boundary conditions. Radiative highly absorbing medium is modeled by the Rosseland approximation. Th...

This paper describes a theoretical study to investigate the heat transfer characteristics of porous radiant burners. A one dimensional model is used to solve the governing equations for porous medium and gas flow before the premixed flame to the exhaust gas. Combustion in the porous medium is modeled as a spatially dependent heat generation zone. The homogeneous porous media, in addition to its...

This article is concerned with Darcy’s law for an incompressible viscous fluid flowing in a porous medium. We establish the sharp O(ε) convergence rate periodically perforated and bounded domain Rd d≥2, where ε represents size of solid obstacles. achieved by constructing two boundary layer correctors to control layers created incompressibility condition discrepancy values between solution leadi...

The present investigation deals with the propagation of Rayleigh wave in an incompressible medium bonded between two half-spaces. Variation in elastic parameters of the layer is taken linear form. The solution for layer and half-space are obtained analytically. Frequency equation for Rayleigh waves has been obtained. It is observed that the heterogeneity and width of the incompressible medium h...

We consider the non stationary flow of a viscous incompressible fluid in a rigid homogeneous porous medium provided with mixed boundary conditions. Since the medium is nonhomogeneous, its permeability is only piecewise continuous. We are thus led to use the mortar method to handle these discontinuities. We propose a space and time discretization of the full system. We prove optimal a priori err...

*Correspondence: Olav Aursjø and Knut J. Måløy, Department of Physics, University of Oslo, PO Box 1048 Blindern, NO-0316 Oslo, Norway e-mail: [email protected]; [email protected] We present an experimental study of two-phase flow in a quasi-two-dimensional porous medium. The two phases, a water-glycerol solution and a commercial food grade rapeseed/canola oil, having an oil to water-gly...

We study the stability of stationary solutions of the 2D inviscid incompressible porous medium equation (IPM). We show that solutions which are near certain stable stationary solutions must converge as t → ∞ to a stationary solution of the IPM equation. It turns out that linearizing the IPM equation about certain stable stationary solutions gives a non-local partial damping mechanism. On the to...