Abstract We establish Hölder continuity for locally bounded weak solutions to certain parabolic systems of porous medium type, i.e. $$\begin{aligned} \partial _t \mathbf{u}-\mathrm{div}(m|\mathbf{u}|^{m-1}D\mathbf{u})=0,\quad m&gt;0. \end{aligned}$$ ∂ t</mml:...

&lt;p style='text-indent:20px;'&gt;We study a porous medium equation with dissipative and hyperdiffusive effects no sign restrictions on the diffusion coefficient.&lt;/p&gt;

Abstract This paper is concerned with the homogenization of model problems in periodic porous media when important phenomena occur on the boundaries of the pores. To this end, we generalize the notion of two-scale convergence for sequences of functions which are defined on periodic surfaces. We apply our results to two model problems : the first one is a diffusion equation in a porous medium wi...

We show that when a non-wetting fluid drains a stratified porous medium at sufficiently small capillary numbers Ca, it flows only through the coarsest stratum of the medium; by contrast, above a threshold Ca, the non-wetting fluid is also forced laterally, into part of the adjacent, finer strata. The spatial extent of this partial invasion increases with Ca. We quantitatively understand this be...

The Faraday rotation angle is calculated in a diffusive regime on a three-dimensional disordered slab. It is shown that tan is (i) an oscillating function of the magnetic field or the medium’s internal properties, and (ii) proportional to the ratio of the inelastic mean-free path lin to the mean-free path l, that is, to the average number of photon scatterings. The maximum rotation is achieved ...

In this paper, the influence of transverse wave on sound propagation in a porous medium with flexible structure is considered. The study carried out time domain using modified Biot theory obtained by symmetry Lagrangian (invariance translation and rotation). viscous exchanges between fluid are described fractional calculus. When pulse arrives at normal incidence material structure, waves interf...

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...