Search results for "UNIQUE"

Well-posedness of the boundary layer equations

2004

We consider the mild solutions of the Prandtl equations on the half space. Requiring analyticity only with respect to the tangential variable, we prove the short time existence and the uniqueness of the solution in the proper function space. Theproof is achieved applying the abstract Cauchy--Kowalewski theorem to the boundary layer equations once the convection-diffusion operator is explicitly inverted. This improves the result of [M. Sammartino and R. E. Caflisch, Comm. Math. Phys., 192 (1998), pp. 433--461], as we do not require analyticity of the data with respect to the normal variable.

Existence and uniqueness for the Prandtl equations

2001

International audience; Under the hypothesis of analyticity of the data with respect to the tangential variable we prove the existence and uniqueness of the mild solution of Prandtl boundary layer equation. This can be considered an improvement of the results of [8] as we do not require analyticity with respect to the normal variable. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.

Le parti des travailleurs brésilien : de son émergence à la conquête du Planalto (1979 - 2002)

2016

The Brazilian Workers’ Party (PT) is an outstanding experience of a left-wing mass party. When it was born in 1980, many people wondered about its nature. In 2002, when Lula became the President of Brazil, this question did not deserve the same answer. The PT became bureaucratic, institutional and professional, experiencing a sort of accelerated Social-Democratization. As its starting point, this study takes the specificities of labour movement, trade unionism and the dictatorship (1964-1985) in Brazil. The PT originated in 1979-80 from mass social struggles around “authentic” trade unionists (such as Lula), left-wing Catholics, far-left activists, the left-wing intelligentsia and some “pro…

2015

In this work we review the mapping from densities to potentials in quantum mechanics, which is the basic building block of time-dependent density-functional theory and the Kohn-Sham construction. We first present detailed conditions such that a mapping from potentials to densities is defined by solving the time-dependent Schrodinger equation. We specifically discuss intricacies connected with the unboundedness of the Hamiltonian and derive the local-force equation. This equation is then used to set up an iterative sequence that determines a potential that generates a specified density via time propagation of an initial state. This fixed-point procedure needs the invertibility of a certain S…

On the Uniqueness of the Energy and Momenta of an Asymptotically Minkowskian Space-Time: The Case of the Schwarzschild Metric

2013

Some theorems about the uniqueness of the energy of asymptotically Minkowskian spaces are recalled. The suitability of almost everywhere Gauss coordinates to define some kind of physical energy in these spaces is commented. Schwarzschild metric, when its source radius is larger than the Schwarzschild radius and in the case of a black hole, is considered. In both cases, by using a specific almost everywhere Gaussian coordinate system, a vanishing energy results. We explain why this result is not in contradiction with the quoted theorems. Finally we conclude that this metric is a particular case of what we have called elsewhere a creatable universe.

Simultaneously recovering potentials and embedded obstacles for anisotropic fractional Schrödinger operators

2017

Let \begin{document}$A∈{\rm{Sym}}(n× n)$\end{document} be an elliptic 2-tensor. Consider the anisotropic fractional Schrodinger operator \begin{document}$\mathscr{L}_A^s+q$\end{document} , where \begin{document}$\mathscr{L}_A^s: = (-\nabla·(A(x)\nabla))^s$\end{document} , \begin{document}$s∈ (0, 1)$\end{document} and \begin{document}$q∈ L^∞$\end{document} . We are concerned with the simultaneous recovery of \begin{document}$q$\end{document} and possibly embedded soft or hard obstacles inside \begin{document}$q$\end{document} by the exterior Dirichlet-to-Neumann (DtN) map outside a bounded domain \begin{document}$Ω$\end{document} associated with \begin{document}$\mathscr{L}_A^s+q$\end{docume…

Multipole solitary wave solutions of the higher-order nonlinear Schrödinger equation with quintic non-Kerr terms

2013

We consider a high-order nonlinear Schrodinger (HNLS) equation with third- and fourth-order dispersions, quintic non-Kerr terms, self steepening, and self-frequency-shift effects. The model applies to the description of ultrashort optical pulse propagation in highly nonlinear media. We propose a complex envelope function ansatz composed of single bright, single dark and the product of bright and dark solitary waves that allows us to obtain analytically different shapes of solitary wave solutions. Parametric conditions for the existence and uniqueness of such solitary waves are presented. The solutions comprise fundamental solitons, kink and anti-kink solitons, W-shaped, dipole, tripole, and…

Analysis of the viscous quantum hydrodynamic equations for semiconductors

2004

The steady-state viscous quantum hydrodynamic model in one space dimension is studied. The model consists of the continuity equations for the particle and current densities, coupled to the Poisson equation for the electrostatic potential. The equations are derived from a Wigner–Fokker–Planck model and they contain a third-order quantum correction term and second-order viscous terms. The existence of classical solutions is proved for “weakly supersonic” quantum flows. This means that a smallness condition on the particle velocity is still needed but the bound is allowed to be larger than for classical subsonic flows. Furthermore, the uniqueness of solutions and various asymptotic limits (sem…

Existence and Uniqueness Results for Quasi-linear Elliptic and Parabolic Equations with Nonlinear Boundary Conditions

2006

We study the questions of existence and uniqueness of weak and entropy solutions for equations of type -div a(x, Du)+γ(u) ∋ φ, posed in an open bounded subset Ω of ℝN, with nonlinear boundary conditions of the form a(x, Du)·η+β(u) ∋ ψ. The nonlinear elliptic operator div a(x, Du) is modeled on the p-Laplacian operator Δp(u) = div (|Du|p−2Du), with p > 1, γ and β are maximal monotone graphs in ℝ2 such that 0 ∈ γ(0) and 0 ∈ β(0), and the data φ ∈ L1 (Ω) and ψ ∈ L1 (∂Ω). We also study existence and uniqueness of weak solutions for a general degenerate elliptic-parabolic problem with nonlinear dynamical boundary conditions. Particular instances of this problem appear in various phenomena with c…

On the Frequency Behaviour, Stability and Isolation Properties of Dry Friction Oscillators

2006

This paper proposes a new approach to the frequency responses of one-degree-of-freedom oscillators subject to periodic excitations in presence of mixed dry-viscous friction. The idea is to get free from the analysis of one fixed system by letting the physical parameters cover their own whole ranges and investigating the various behavioural aspects of wide classes of oscillators. The existence, uniqueness and stability of the steady-state solutions are analysed in detail, assuming different coefficients of static and sliding friction. The possible arising of motions characterized by anti-periodic asymmetry or multi-stick oscillations is enlightened and maps of the system behaviour are presen…