Browsing Past Topics (PT) by Issue Date
Now showing items 120 of 220

Identification of the class of initial data for the insensitizing control of the heat equation
(Communications on Pure and Applied Analysis, 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 ... 
Time discrete wave equations: Boundary observability and control
(Discrete and Continuous Dynamical Systems, 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 ... 
Convergence of a twogrid algorithm for the control of the wave equation
(Journal of the European Mathematical Society, 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 ... 
Numerical dispersive schemes for the nonlinear Schrödinger equation
(SIAM Journal on Numerical Analysis, 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 ... 
Uniformly exponentially stable approximations for a class of damped systems
(Journal des Mathematiques Pures et Appliquees, 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 ... 
Homogenization of fiber reinforced brittle materials: The extremal cases
(SIAM Journal on Mathematical Analysis, 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: ... 
Minimization of length and curvature on planar curves
(Proceedings of the IEEE Conference on Decision and Control, 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 ... 
Stabilization of the wave equation on 1D networks
(SIAM Journal on Control and Optimization, 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. ... 
Some controllability results for the 2D Kolmogorov equation
(Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, 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 ... 
Hardy inequalities, observability, and control for the wave and schrödinger equations with singular potentials
(SIAM Journal on Mathematical Analysis, 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 ... 
Asymptotic stability of the stationary solution to an initial boundary value problem for the Mullins equation of fourth order
(Journal of Mathematical Physics, 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 ... 
2D euler shape design on nonregular flows using adjoint rankinehugoniot relations
(AIAA Journal, 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 rarefaction wave for the navierstokes equations for a compressible fluid in the half space
(Archive for Rational Mechanics and Analysis, 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. ... 
Numerical approximation of null controls for the heat equation : Illposedness and remedies
(Inverse Problems, 20101231)The numerical approximation of exact or trajectory controls for the wave equation is known to be a delicate issue, since the pioneering work of GlowinskiLions in the nineties, because of the anomalous behavior of the ... 
Stationary waves to viscous heatconductive gases in halfspace: Existence, stability and convergence rate
(Mathematical Models and Methods in Applied Sciences, 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
(Multiscale Modeling and Simulation, 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 ... 
Asymptotic limits and stabilization for the 1D nonlinear MindlinTimoshenko system
(Journal of Systems Science and Complexity, 20101231)This paper shows how the so called von Kármán model can be obtained as a singular limit of a modified MindlinTimoshenko system when the modulus of elasticity in shear k tends to infinity, provided a regularizing term ... 
A systematic method for building smooth controls for smooth data
(Discrete and Continuous Dynamical Systems  Series B, 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 ... 
The Hardy inequality and the heat equation in twisted tubes
(Journal des Mathematiques Pures et Appliquees, 20101231)We show that a twist of a threedimensional tube of uniform crosssection yields an improved decay rate for the heat semigroup associated with the Dirichlet Laplacian in the tube. The proof employs Hardy inequalities for ... 
Mathematical Models of Incompressible Fluids as Singular Limits of Complete Fluid Systems
(Milan Journal of Mathematics, 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 ...