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The influence of slip boundary effect on the propagation of shear horizontal guided waves in a fluid-saturated porous medium
Studies on the wetting effect reveal that slip is prevalent at the fluid–solid interface, and its influence cannot be disregarded in microscopic...
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Flow and heat transfer of a nanofluid through a porous medium due to stretching/shrinking sheet with suction, magnetic field and thermal radiation
This study investigates the suction and magnetic field effects on the two-dimensional nanofluid flow through a stretching/shrinking sheet at the...
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Natural Convection Flow in an Inclined Wavy Porous Medium in the Presence of an Inclined Periodic Magnetic Field
In this study, unsteady natural convection flow in an inclined porous wavy cavity under the effect of an inclined periodic magnetic field (MF) is...
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Porous Materials
A porous material is a substance that contains pores, or spaces, between solid materials through which liquid or gas can flow. Examples of naturally...
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On the Hölder regularity for obstacle problems to porous medium type equations
We show that signed weak solutions to parabolic obstacle problems with porous medium-type structure are locally Hölder continuous, provided that the...
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Analysis of magnetized Rayleigh–Taylor instability in nanofluids through porous medium
The current study introduces the Rayleigh–Taylor instability of two overlaying nanofluids (horizontally) possessing different densities with the...
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Continuous data assimilation for displacement in a porous medium
In this paper we propose the use of a continuous data assimilation algorithm for miscible flow models in a porous medium. In the absence of initial...
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Gradient Flows of Modified Wasserstein Distances and Porous Medium Equations with Nonlocal Pressure
We study families of porous medium equations with nonlocal pressure. We construct their weak solutions via JKO schemes for modified Wasserstein...
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An optimal Liouville theorem for the porous medium equation
Under a sharp asymptotic growth condition at infinity, we prove a Liouville type theorem for the inhomogeneous porous medium equation, provided it...
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Transient MHD Free Convection Flow, Heat and Mass Transfer in Darcy–Forchheimer Porous Medium in the Presence of Chemical Reaction and Heat Absorption with Soret and Dufour Effects: Element-Free Galerkin Modelling
AbstractThe effects of diffuso-thermal (Dufour effect) and thermo-diffusion gradients (Soret effect) on the magneto-hydrodynamic (MHD) unsteady...
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Neural Network-Based Variational Methods for Solving Quadratic Porous Medium Equations in High Dimensions
In this paper, we propose and study neural network-based methods for solutions of high-dimensional quadratic porous medium equation (QPME). Three...
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MHD Flow Through a Perturbed Channel Filled with a Porous Medium
The main aim of this paper is to investigate the effects of a slightly perturbed boundary on the MHD flow through a channel filled with a porous...
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Elastic Waves in a Porous Medium with Layers of Different Permeabilities
AbstractA two-dimensional axisymmetric problem of pressure wave propagation in a porous medium of a layered structure is considered. The wave...
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Mathematical Modeling of Gas Hydrate Dissociation in Porous Medium Taking into Account Ice and Salinity
AbstractThis work is devoted to the mathematical modeling of the dissociation of gas hydrates in a porous medium. Numerical methods are developed for...
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The well-posedness problem of an anisotropic porous medium equation with a convection term
The initial boundary value problem of an anisotropic porous medium equation is considered in this paper. The existence of a weak solution is proved...
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Impact of Magnetic Field on the Flow of a Conducting Fluid Past an Impervious Spheroid Embedded in Porous Medium
The majority of the previous studies analyzed the flow of fluid around the perfect sphere however the slight deformations in the shape of the...
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The fractional porous medium equation on manifolds with conical singularities I
This is the first of a series of two papers which studies the fractional porous medium equation on a Riemannian manifold with isolated conical...