The approximation of the pressure by a mixed method in the simulation of miscible displacement
The behavior of the free boundary for the dam problem
The dam problem for nonlinear Darcy's laws and Dirichlet boundary conditions
The dipole solution for the porous medium equation in several space dimensions
The effect of Coriolis force on nonlinear convection in a porous medium.
The evolution dam problem for nonlinear Darcy's law and Dirichlet boundary conditions.
The finite volume method for an elliptic-parabolic equation.
The flow of a non-Newtonian fluid induced due to the oscillations of a porous plate.
The Fluid Flow Through Porous Media. Regularity of the Free Surface.
The generalized finite volume SUSHI scheme for the discretization of the peaceman model
We demonstrate some a priori estimates of a scheme using stabilization and hybrid interfaces applying to partial differential equations describing miscible displacement in porous media. This system is made of two coupled equations: an anisotropic diffusion equation on the pressure and a convection-diffusion-dispersion equation on the concentration of invading fluid. The anisotropic diffusion operators in both equations require special care while discretizing by a finite volume method SUSHI. Later,...
The inhomogeneous dam problem with discontinuous permeability
The porous medium equation as a finite-speed approximation to a Hamilton-Jacobi equation
The problem of data assimilation for soil water movement
The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented.
The problem of data assimilation for soil water movement
The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented.
The relation between the porous medium and the eikonal equations in several space dimensions.
We study the relation between the porous medium equation ut = Δ(um), m > 1, and the eikonal equation vt = |Dv|2. Under quite general assumtions, we prove that the pressure and the interface of the solution of the Cauchy problem for the porous medium equation converge as m↓1 to the viscosity solution and the interface of the Cauchy problem for the eikonal equation. We also address the same questions for the case of the Dirichlet boundary value problem.
The Rothe method for solving the first initial-boundary value problem for the equation of filtration in a cracked porous medium.
Theoretical analysis of a model of the thermal boundary layer with drag.
Thermal radiation and MHD effects on free convective flow of a polar fluid through a porous medium in the presence of internal heat generation and chemical reaction.
Thermal radiation effects on hydromagnetic mixed convection flow along a magnetized vertical porous plate.
Three-dimensional fluctuating Couette flow through the porous plates with heat transfer.