On the second order slip Reynolds equation with molecular dynamics: existence and uniqueness.
On the Semigroup of the Stokes Operator for Exterior Domains in Lq-Spaces.
On the simulation of incompressible, miscible displacement in a naturally fractured petroleum reservoir
On the smallness of the (possible) singular set in space for 3D Navier-Stokes equations.
On the solution of a differential equation occurring in the problem of heat convection in laminar flow through a tube with slip-flow.
On the solution of linear algebraic systems arising from the semi–implicit DGFE discretization of the compressible Navier–Stokes equations
We deal with the numerical simulation of a motion of viscous compressible fluids. We discretize the governing Navier–Stokes equations by the backward difference formula – discontinuous Galerkin finite element (BDF-DGFE) method, which exhibits a sufficiently stable, efficient and accurate numerical scheme. The BDF-DGFE method requires a solution of one linear algebra system at each time step. In this paper, we deal with these linear algebra systems with the aid of an iterative solver. We discuss...
On the solution of reaction-diffusion equations with double diffusivity.
On the solution of some inverse problems in infiltration
In this paper we discuss inverse problems in infiltration. We propose an efficient method for identification of model parameters, e.g., soil parameters for unsaturated porous media. Our concept is strongly based on the finite speed of propagation of the wetness front during the infiltration into a dry region. We determine the unknown parameters from the corresponding ODE system arising from the original porous media equation. We use the automatic differentiation implemented in the ODE solver LSODA....
On the solution of some inverse problems in porous media flow.
On the solution of transonic flows with weak shocks
On the solvability of a problem of stationary fluid flow in a helical pipe.
On the solvability of some initial boundary value problems of magnetofluidmechanics with Hall and ion-slip effects
The solvability of three linear initial-boundary value problems for the system of equations obtained by linearization of MHD equations is established. The equations contain terms corresponding to Hall and ion-slip currents. The solutions are found in the Sobolev spaces with and in anisotropic Holder spaces.
On the space-time permeated by a viscous, compressible, thermally conducting, self-gravitating fluid with infinite electrical conductivity and constant magnetic permeability
On the spatially homogeneous Boltzmann equation
On the Stability of Bilinear-Constant Velocity-Pressure Finite Elements.
On the stability of compressible Navier-Stokes-Korteweg equations
We consider the compressible Navier-Stokes-Korteweg (N-S-K) equations. Through a remarkable identity, we reveal a relationship between the quantum hydrodynamic system and capillary fluids. Using some interesting inequalities from quantum fluids theory, we prove the stability of weak solutions for the N-S-K equations in the periodic domain , when N=2,3.
On the stability of stellar structure in one dimension II : the reactive case
On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations
We consider the coupling between three-dimensional (3D) and one-dimensional (1D) fluid-structure interaction (FSI) models describing blood flow inside compliant vessels. The 1D model is a hyperbolic system of partial differential equations. The 3D model consists of the Navier-Stokes equations for incompressible Newtonian fluids coupled with a model for the vessel wall dynamics. A non standard formulation for the Navier-Stokes equations is adopted to have suitable boundary conditions for the...
On the stationary Boltzmann equation
For stationary kinetic equations, entropy dissipation can sometimes be used in existence proofs similarly to entropy in the time dependent situation. Recent results in this spirit obtained in collaboration with A. Nouri, are here presented for the nonlinear stationary Boltzmann equation in bounded domains of with given indata and diffuse reflection on the boundary.
On the stationary motion of compressible viscous fluids