Browsing Past Topics (PT) by Issue Date
Now showing items 1-20 of 220
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Convergence of a two-grid algorithm for the control of the wave equation
(2009-12-31)We analyze the problem of boundary observability of the finite-difference space semidiscretizations of the 2-d 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
(2009-12-31)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 ... -
Asymptotic stability of rarefaction wave for the navier-stokes equations for a compressible fluid in the half space
(2009-12-31)This paper is concerned with the asymptotic stability towards a rarefaction wave of the solution to an outflow problem for the Navier-Stokes equations in a compressible fluid in the Eulerian coordinate in the half space. ... -
Uniformly exponentially stable approximations for a class of damped systems
(2009-12-31)We consider time semi-discrete approximations of a class of exponentially stable infinite-dimensional systems modeling, for instance, damped vibrations. It has recently been proved that for time semi-discrete systems, due ... -
Numerical dispersive schemes for the nonlinear Schrödinger equation
(2009-12-31)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 1-D networks
(2009-12-31)In this paper we study the stabilization of the wa ve equation on general 1-d networks. For that, we transfer known observability results in the context of control problems of conservative systems (see [R. Dáger and E. ... -
Homogenization of fiber reinforced brittle materials: The extremal cases
(2009-12-31)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
(2009-12-31)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 ... -
Identification of the class of initial data for the insensitizing control of the heat equation
(2009-12-31)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 ... -
Hardy inequalities, observability, and control for the wave and schrödinger equations with singular potentials
(2009-12-31)We address the question of exact controllability of the wave and Schrodinger equa\-tions perturbed by a singular inverse-square potential. Exact boundary controllability is proved in the range of subcritical coefficients ... -
Some controllability results for the 2D Kolmogorov equation
(2009-12-31)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 right-hand side of the equation, located on a subdomain, that ... -
2-D euler shape design on nonregular flows using adjoint rankine-hugoniot relations
(2009-12-31)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
(2009-12-31)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 ["Two-dimensional motion of idealized ... -
Stationary waves to viscous heat-conductive gases in half-space: Existence, stability and convergence rate
(2010-12-31)The main concern of this paper is to study large-time behavior of solutions to an ideal polytropic model of compressible viscous gases in one-dimensional half-space. We consider an outflow problem and obtain a convergence ... -
Invertibility and weak continuity of the determinant for the modelling of cavitation and fracture in nonlinear elasticity
(2010-12-31)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
(2010-12-31)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 energy-minimizers 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]
(2010-12-31)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 ... -
A variational model for infin ite perimeter segmentations based on lipschitz level set functions: Denoising while keeping finely oscillatory boundaries
(2010-12-31)We propose a new model for segmenting piecewise constant images with irregular object boundaries: a variant of the Chan-Vese model [T. F. Chan and L. A. Vese, IEEE Trans. Image Process., 10 (2000), pp. 266-277], where the ... -
Asymptotic limits and stabilization for the 1D nonlinear Mindlin-Timoshenko system
(2010-12-31)This paper shows how the so called von Kármán model can be obtained as a singular limit of a modified Mindlin-Timoshenko system when the modulus of elasticity in shear k tends to infinity, provided a regularizing term ... -
Strichartz estimates for the Schrödinger equation on a tree and applications
(2010-12-31)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 Strichartz-like estimates for the linear semigroup and apply them to ...