We study the asymptotic behavior of compressible isentropic flow through porous medium with general L∞ initial data. The model system is the compressible Euler equation with frictional damping. As t → ∞, the density is conjectured to obey to the well-known porous medium equation and the momentum is expected to be formulated by Darcy’s law. Recent progress gives a definte answer to this conjectu...

A linear stability analysis is applied to a system consisting of three horizontal layers, a viscous fluid layer sandwiched between two porous medium permeated by the fluid that the lower layer is heated uniformlly from below. Flow in the porous medium is assumed to be governed by Darcy’s law. The Beavers-Joseph condition is applied at the interface between any two different layers.Spectral meth...

Numerous techniques have been presented by different researchers to analyze piled raft. In order to analyze pile foundation, soil can be modeled as spring, continuous medium, or porous media. Pile can also be modeled as spring or continuous medium. This study includes three main stages: a short description of different types of analysis methods of pile foundation, writing a computer program bas...

In this paper we are interested with a strongly coupled system of partial differential equations that modelizes free convection in a two-dimensional bounded domain filled with a fluid saturated porous medium. This model is inspired by the one of free convection near a semi-infinite impermeable vertical flat plate embedded in a fluid saturated porous medium. We establish the existence and unique...

The paper first discusses the real fluids circulating in the earth’s crust, and justifies the need to examine the natural convection in a porous medium of a simple pure fluid with properties resembling those near the thermodynamic critical point. The literature on natural convection in a homogenous porous medium between isothermal horizontal plates, the lower one hotter, is then reviewed. Resul...

Granular mixtures segregate radially by size when tumbled in a partially filled horizontal drum. The smaller component moves toward the axis of rotation and forms a buried core, which then splits into axial bands. Models have generally assumed that the axial segregation is opposed by diffusion. Using narrow pulses of the smaller component as initial conditions, we have characterized axial trans...

We review some lines of recent research in the theory of the porous medium equation. We then proceed to discuss the question of contractivity with respect to the Wasserstein metrics: we show contractivity in one space dimension in all distances dp, 1 ≤ p ≤ ∞, and show a negative result for the d∞ metric in several dimensions. We end with a list of problems. Mathematics Subject Classification. 3...

In this paper, we study with a periodic porous medium equation with nonlinear convection terms and weakly nonlinear sources under Dirichlet boundary conditions. Based on the theory of Leray-Shauder fixed point theorem, we establish the existence of periodic solutions.

Porous Silicon (PS) layers have been prepared from p-type silicon wafers of (100) orientation. SEM, XRD, FTIR and PL studies were done to characterize the surface morphological and optical properties of PS. The porosity of the PS samples was determined using the parameters obtained from SEM images by geometric method. The refractive index values of the PS samples as a function of poros...

We consider the porous medium equation on a compact Riemannian manifold and give a new proof of the contraction of its semigroup in the Wasserstein distance. This proof is based on the insight that the porous medium equation does not increase the size of infinitesimal perturbations along gradient flow trajectories, and on an Eulerian formulation for the Wasserstein distance using smooth curves....