An approach by difference to the porous medium equation with convection

Mixed Entropy Estimates for the Porous-medium Equation with Convection

In this paper, we answer the question under which conditions the porousmedium equation with convection and with periodic boundary conditions possesses gradient-type Lyapunov functionals (first-order entropies). It is shown that the weighted sum of first-order and zeroth-order entropies are Lyapunov functionals if the weight for the zeroth-order entropy is sufficiently large, depending on the st...

The Porous Medium Equation with Measure Data

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...

The Density-Driven Nanofluid Convection in an Anisotropic Porous Medium Layer with Rotation and Variable Gravity Field: A Numerical Investigation

In this study, a numerical examination of the significance of rotation and changeable gravitational field on the start of nanofluid convective movement in an anisotropic porous medium layer is shown. A model that accounts for the impact of Brownian diffusion and thermophoresis is used for nanofluid, while Darcy’s law is taken for the porous medium. The porous layer is subjected to uniform rotat...

Chemically Driven Convection in a Porous Medium

On the finite difference approximation to the convection-diffusion equation

In this paper, the system of ordinary differential equations arisen from discretizing the convection-diffusion equation with respect to the space variable to compute its approximate solution along a time level is considered. This system involves in computing ey for some vector y, where k is the time step-size and A is a large tridiagonal Toeplitz matrix. The common ways to compute an approximat...