Mapping properties of regular and strongly degenerate elliptic differential operators in the Besov spaces . The case
Mappings of monotone type: Theory and applications
Maps and fields with compressible density
Marchuk identity-type second order difference schemes of 2-d and 3-d elliptic problems with intersected interfaces
Martin boundary for Schrödinger operators with singularity.
Martin compactification and asymptotics of Green functions for Schrödinger operators with anisotropic potentials.
Matching of asymptotic expansions for waves propagation in media with thin slots II: The error estimates
We are concerned with a 2D time harmonic wave propagation problem in a medium including a thin slot whose thickness ε is small with respect to the wavelength. In a previous article, we derived formally an asymptotic expansion of the solution with respect to ε using the method of matched asymptotic expansions. We also proved the existence and uniqueness of the terms of the asymptotics. In this paper, we complete the mathematical justification of our work by deriving optimal error estimates between...
Matematické modely a numerické simulace vln cunami
Matematik Jindřich Nečas
Matematika hudebních nástrojů
Mathematical analysis and numerical simulation of a Reynolds-Koiter model for the elastohydrodynamic journal-bearing device
The aim of this work is to deduce the existence of solution of a coupled problem arising in elastohydrodynamic lubrication. The lubricant pressure and concentration are modelled by Reynolds equation, jointly with the free-boundary Elrod-Adams model in order to take into account cavitation phenomena. The bearing deformation is solution of Koiter model for thin shells. The existence of solution to the variational problem presents some difficulties: the coupled character of the equations, the nonlinear...
Mathematical analysis and numerical simulation of a Reynolds-Koiter model for the elastohydrodynamic journal-bearing device
The aim of this work is to deduce the existence of solution of a coupled problem arising in elastohydrodynamic lubrication. The lubricant pressure and concentration are modelled by Reynolds equation, jointly with the free-boundary Elrod-Adams model in order to take into account cavitation phenomena. The bearing deformation is solution of Koiter model for thin shells. The existence of solution to the variational problem presents some difficulties: the coupled character of the equations, the nonlinear...
Mathematical analysis of a discrete fracture model coupling Darcy flow in the matrix with Darcy–Forchheimer flow in the fracture
We consider a model for flow in a porous medium with a fracture in which the flow in the fracture is governed by the Darcy−Forchheimerlaw while that in the surrounding matrix is governed by Darcy’s law. We give an appropriate mixed, variational formulation and show existence and uniqueness of the solution. To show existence we give an analogous formulation for the model in which the Darcy−Forchheimerlaw is the governing equation throughout the domain. We show existence and uniqueness of the solution...
Mathematical analysis of a finite element method without spurious solutions for computation of dielectric waveguides.
Mathematical analysis of a spectral hyperviscosity LES model for the simulation of turbulent flows
This paper presents a model based on spectral hyperviscosity for the simulation of 3D turbulent incompressible flows. One particularity of this model is that the hyperviscosity is active only at the short velocity scales, a feature which is reminiscent of Large Eddy Simulation models. We propose a Fourier–Galerkin approximation of the perturbed Navier–Stokes equations and we show that, as the cutoff wavenumber goes to infinity, the solution of the model converges (up to subsequences) to a weak solution...
Mathematical analysis of a spectral hyperviscosity LES model for the simulation of turbulent flows
This paper presents a model based on spectral hyperviscosity for the simulation of 3D turbulent incompressible flows. One particularity of this model is that the hyperviscosity is active only at the short velocity scales, a feature which is reminiscent of Large Eddy Simulation models. We propose a Fourier–Galerkin approximation of the perturbed Navier–Stokes equations and we show that, as the cutoff wavenumber goes to infinity, the solution of the model converges (up to subsequences) to a weak...
Mathematical analysis of a two-phase parabolic free boundary problem derived from a Bingham-type model with visco-elastic core
In this paper we consider a two-phase one-dimensional free boundary problem for the heat equation, arising from a mathematical model for a Bingham-like fluid with a visco-elastic core. The main feature of this problem consists in the very peculiar structure of the free boundary condition, not allowing to use classical tools to prove well posedness. Existence of classical solution is proved using a fixed point argument based on Schauder's theorem. Uniqueness is proved using a technique based on a...
Mathematical analysis of electromagnetic open Waveguides
Mathematical analysis of the discharge of a laminar hot gas in a colder atmosphere.
We study the boundary layer approximation of the, already classical, mathematical model which describes the discharge of a laminar hot gas in a stagnant colder atmosphere of the same gas. We start by proving the existence and uniqueness of solutions of the nondegenerate problem under assumptions implying that the temperature T and the horizontal velocity u of the gas are strictly positive: T ≥ δ > 0 and u ≥ ε > 0 (here δ and ε are given as boundary conditions in the external atmosphere)....
Mathematical analysis of the stabilization of lamellar phases by a shear stress
We consider a 2D mathematical model describing the motion of a solution of surfactants submitted to a high shear stress in a CouetteTaylor system. We are interested in a stabilization process obtained thanks to the shear. We prove that, if the shear stress is large enough, there exists global in time solution for small initial data and that the solution of the linearized system (controlled by a nonconstant parameter) tends to 0 as goes to infinity. This explains rigorously some experiments.