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;

In this work a glass micromodel which its grains and pores are non-uniform in size, shape and distribution is considered as porous medium. A two-dimensional random network model of micromodel with non-uniform pores has been constructed. The non-uniformity of porous model is achieved by assigning parametric distribution functions to pores throat and pores length, which was measured using ima...

To characterize the velocity slip at the fibrous porous media, data on the anisotropic slip length has been fully analyzed through direct simulations for various geometrical aspects of fiber architecture [2] ). This data article provides detailed slip lengths and slip coefficients in dimensionless form as a function of various geometrical parameters of fibrous porous media including the fiber v...

Control strategy on Rayleigh-Benard convection in rotating nanofluids saturated anisotropic porous layer heated from below is studied the presence of uniformly internal heat source for rigid-rigid, free-free, and lower-rigid upper-free boundaries. Feedback control with an array sensors situated at top plate actuators located bottom are considered this study. Linear stability analysis based norm...

Understanding the transport properties of a porous medium from a knowledge of its microstructure is a problem of great interest in the physical, chemical, and biological sciences. Using a first-passage time method, we compute the mean survival time tau of a Brownian particle among perfectly absorbing traps for a wide class of triply periodic porous media, including minimal surfaces. We find tha...

Constant flux atom deposition into a porous medium is shown to generate a dense overlayer and a diffusion profile. Scaling analysis shows that the overlayer acts as a dynamic control for atomic diffusion in the porous substrate. This is modeled by generalizing the porous diffusion equation with a time-dependent diffusion coefficient equivalent to a nonlinear rescaling of time.

In tissue engineering, porous biodegradable scaffolds are used as templates for regenerating required tissues. With the advances in computational tools, many modeling approaches have been considered. For example, fluid flow through porous medium can be modeled using the Brinkman equation where permeability of the porous medium has to be defined. In this review, we summarize various models recen...