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Asymptotic stability of rarefaction wave for the navierstokes equations for a compressible fluid in the half space
(20091231)This paper is concerned with the asymptotic stability towards a rarefaction wave of the solution to an outflow problem for the NavierStokes equations in a compressible fluid in the Eulerian coordinate in the half space. ... 
Convergence of a twogrid algorithm for the control of the wave equation
(20091231)We analyze the problem of boundary observability of the finitedifference space semidiscretizations of the 2d wave equation in the square.We prove the uniform (with respect to the meshsize) boundary observability for the ... 
Time discrete wave equations: Boundary observability and control
(20091231)In this paper we study the exact boundary controllability of a trapezoidal time discrete wave equation in a bounded domain. We prove that the projection of the solution in an appropriate filtered space is exactly controllable ... 
Uniformly exponentially stable approximations for a class of damped systems
(20091231)We consider time semidiscrete approximations of a class of exponentially stable infinitedimensional systems modeling, for instance, damped vibrations. It has recently been proved that for time semidiscrete systems, due ... 
Minimization of length and curvature on planar curves
(20091231)In this paper we consider the problem of reconstructing a curve that is partially hidden or corrupted by minimizing the functional ∫ √1+K 2 ds, depending both on length and curvature K. We fix starting and ending points ... 
Homogenization of fiber reinforced brittle materials: The extremal cases
(20091231)We analyze the behavior of a fragile material reinforced by a reticulated elastic unbreakable structure in the case of antiplane shear. The microscopic geometry of this material is described by means of two small parameters: ... 
Hardy inequalities, observability, and control for the wave and schrödinger equations with singular potentials
(20091231)We address the question of exact controllability of the wave and Schrodinger equa\tions perturbed by a singular inversesquare potential. Exact boundary controllability is proved in the range of subcritical coefficients ... 
Some controllability results for the 2D Kolmogorov equation
(20091231)In this article, we prove the null controllability of the 2D Kolmogorov equation both in the whole space and in the square. The control is a source term in the righthand side of the equation, located on a subdomain, that ... 
Numerical dispersive schemes for the nonlinear Schrödinger equation
(20091231)We consider semidiscrete approximation schemes for the linear Schrödinger equation and analyze whether the classical dispersive properties of the continuous model hold for these approximations. For the conservative finite ... 
Stabilization of the wave equation on 1D networks
(20091231)In this paper we study the stabilization of the wa ve equation on general 1d networks. For that, we transfer known observability results in the context of control problems of conservative systems (see [R. Dáger and E. ... 
2D euler shape design on nonregular flows using adjoint rankinehugoniot relations
(20091231)Optimal aerodynamic shape design aims to find the minimum of a functional that describes an aerodynamic property, by controlling the partial differential equation modeling the dynamics of the flow that surrounds an aircraft, ... 
Asymptotic stability of the stationary solution to an initial boundary value problem for the Mullins equation of fourth order
(20091231)In the present article we first study the existence of the stationary solution to an initial boundary value problem for the Mullins equation of fourth order, which was proposed by Mullins ["Twodimensional motion of idealized ... 
Identification of the class of initial data for the insensitizing control of the heat equation
(20091231)This paper is devoted to analyze the class of initial data that can be insensitized for the heat equation. This issue has been extensively addressed in the literature both in the case of complete and approximate insensitization ... 
Invertibility and weak continuity of the determinant for the modelling of cavitation and fracture in nonlinear elasticity
(20101231)In this paper, we present and analyze a variational model in nonlinear elasticity that allows for cavitation and fracture. The main idea in unifying the theories of cavitation and fracture is to regard both cavities and ... 
A systematic method for building smooth controls for smooth data
(20101231)We prove a regularity result for an abstract control problem z' = Az + Bv with initial datum z(0) = z0 in which the goal is to determine a control v such that z(T) = 0. Under standard admissibility and observability ... 
Explicit energyminimizers of incompressible elastic brittle bars under uniaxial extension [Minimiseurs de l'énergie explicits d'une barre incompressible, élastique, mais fragile, soumise à une extension uniaxiale]
(20101231)A rectangular bar made of a hyperelastic, but brittle, incompressible homogeneous and isotropic material is subject to uniaxial extension. We prove that the energy minimizers are, depending on the toughness coefficient of ... 
Stationary waves to viscous heatconductive gases in halfspace: Existence, stability and convergence rate
(20101231)The main concern of this paper is to study largetime behavior of solutions to an ideal polytropic model of compressible viscous gases in onedimensional halfspace. We consider an outflow problem and obtain a convergence ... 
A variational model for infin ite perimeter segmentations based on lipschitz level set functions: Denoising while keeping finely oscillatory boundaries
(20101231)We propose a new model for segmenting piecewise constant images with irregular object boundaries: a variant of the ChanVese model [T. F. Chan and L. A. Vese, IEEE Trans. Image Process., 10 (2000), pp. 266277], where the ... 
Mathematical Models of Incompressible Fluids as Singular Limits of Complete Fluid Systems
(20101231)A rigorous justification of several wellknown mathematical models of incompressible fluid flows can be given in terms of singular limits of the scaled NavierStokesFourier system, where some of the characteristic numbers ... 
Strichartz estimates for the Schrödinger equation on a tree and applications
(20101231)In this paper, we consider the Schrödinger equation on a network formed by a tree with the last generation of edges formed by infinite strips. We obtain Strichartzlike estimates for the linear semigroup and apply them to ...