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.
To the problem of distribution of structural components of a capillary porous medium.
Travelling waves for gas-solid reactions.
Bounded traveling waves, arising in combustion model for gas-solid reactions in a porous medium, are studied. We consider the existence, uniqueness and several qualitative properties. In particular we investigate waves with finiteness and derive estimates in the limit of vanishing diffusion.
Třicet let matematické teorie metody konečných prvků (medailon prof. M. Zlámala)
Two problems in homogenization of porous media.
The main goal of this work is to present two different problems arising in Fluid Dynamics of perforated domains or porous media. The first problem concerns the compressible flow of an ideal gas through a porous media and our goal is the mathematical derivation of Darcy's law. This is relevant in oil reservoirs, agriculture, soil infiltration, etc. The second problem deals with the incompressible flow of a fluid reacting with the exterior of many packed solid particles. This is related with absorption...
Two-scale convergence of a model for flow in a partially fissured medium.
Un résultat d'existence de solution faible d'un système parabolique-elliptique non linéaire doublement dégénéré
Uniqueness and stability of regional blow-up in a porous-medium equation
Uniqueness of the solution of the Cauchy problem to some equations of nonstationary filtration
Unsteady flow induced by variable suction on a porous disk rotating eccentrically with a fluid at infinity.
Unsteady solutions in a third-grade fluid filling the porous space.