The well-posedness problem of an anisotropic porous medium equation with a convection term

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...

Well-posedness of a fractional porous medium equation on an evolving surface

We investigate the existence, uniqueness, and L-contractivity of weak solutions to a porous medium equation with fractional diffusion on an evolving hypersurface. To settle the existence, we reformulate the equation as a local problem on a semi-infinite cylinder, regularise the porous medium nonlinearity and truncate the cylinder. Then we pass to the limit first in the truncation parameter and ...

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...

Investigation of Natural Convection in a Vertical Cavity Filled with a Anisotropic Porous Media

In present paper, a numerical analysis for a rectangular cavity filled with a anisotropic porous media has been studied. It is assumed that the horizontal walls are adiabatic and impermeable, while the side walls of the cavity are maintained at constant temperatures and concentrations. The buoyancy force that induced the fluid motion are assumed to be cooperative. In the two extreme cases o...

The well-posedness of an anisotropic parabolic equation based on the partial boundary value condition