this work presents the heat transfer characteristics of a new type of porous radiant air heater that operates on the basis of effective energy conversion method between flowing gas enthalpy and thermal radiation. at each layer, the gas and solid phases are considered in non-local thermal equilibrium, and combustion in the porous radiant burner is modeled by considering a non-uniform heat genera...

The plane strain deformation of an isotropic, homogeneous, poroelastic medium caused by an inclined line-load is studied using the Biot linearized theory for fluid saturated porous materials. The analytical expressions for the displacements and stresses in the medium are obtained by applying suitable boundary conditions. The solutions are obtained analytically for the limiting case of undrained...

The objective of the present chapter is to analyze the radiation and mass transfer effects on an unsteady two-dimensional laminar mixed convective boundary layer flow of a viscous, incompressible, electrically conducting chemically reacting fluid, along a vertical moving semi-infinite permeable plate with suction, embedded in a uniform porous medium, in the presence of transverse magnetic field...

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.

To improve the feasibility of soil-aquifer remediation using bioaugmentation, more efficient methods are needed to widely disperse pollutant-degrading bacteria in porous media. Under water-saturated conditions, bacteria readily adhere to soil particles, but under unsaturated conditions, bacteria preferentially accumulate at the air-water interface. Air sparging a saturated porous medium produce...

R J(x − y)u(x, t)dy is the rate at which they are leaving location x to travel to all other sites. This consideration, in the absence of external sources, leads immediately to the fact that the density u satisfies equation (1.1). Throughout this note we shall assume also that J is a decreasing radial function whose support is the unit ball. Under these hypotheses we have that individuals that a...

In this paper, we are interested in the one-dimensional porous medium equation when the initial condition is the distribution function of a probability measure. We associate a nonlinear martingale problem with it. After proving uniqueness for the martingale problem, we show existence owing to a propagation of chaos result for a system of weakly interacting di usion processes. The particle syste...

A simplified model for bacterial remediation of wastes in a porous medium is proposed. The mathematical model consists of a coupled set of nonlinear partial differential equations and an ordinary differential equation. Basic existence, uniqueness and regularity of the system can be proved in three space dimensions, globally in time. The existence of traveling waves can also be established. In a...

We study the existence of solutions to the porous medium equation with a nonnegative, finite Radon measure on the right hand side. We show that such problems have solutions in a wide class of supersolutions. These supersolutions are defined as lower semicontinuous functions obeying a parabolic comparison principle with respect to continuous solutions. We also consider the question of how the in...