Browsing Past Topics (PT) by Issue Date

Some controllability results for the 2D Kolmogorov equation

Beauchard, K.; Zuazua, E. (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 ...

Minimization of length and curvature on planar curves

Boscain, U.; Charlot, G.; Rossi, F. (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 ...

Asymptotic stability of the stationary solution to an initial boundary value problem for the Mullins equation of fourth order

Zhu, P. (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 ...

Time discrete wave equations: Boundary observability and control

Zhang, X.; Zheng, C.; Zuazua, E. (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 ...

Numerical dispersive schemes for the nonlinear Schrödinger equation

Ignat, L.I.; Zuazua, E. (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 ...

Hardy inequalities, observability, and control for the wave and schrödinger equations with singular potentials

Vancostenoble, J.; Zuazua, E. (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 ...

Convergence of a two-grid algorithm for the control of the wave equation

Ignat, L.I.; Zuazua, E. (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 ...

Stabilization of the wave equation on 1-D networks

Valein, J.; Zuazua, E. (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

Barchiesi, M.; Dal Maso, G. (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: ...

Asymptotic stability of rarefaction wave for the navier-stokes equations for a compressible fluid in the half space

Kawashima, S.; Zhu, P. (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. ...

Identification of the class of initial data for the insensitizing control of the heat equation

De Teresa, L.; Zuazua, E. (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 ...

2-D euler shape design on nonregular flows using adjoint rankine-hugoniot relations

Baeza, A.; Castro, C.; Palacios, F.; Zuazua, E. (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, ...

Uniformly exponentially stable approximations for a class of damped systems

Ervedoza, S.; Zuazua, E. (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 ...

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]

Mora-Corral, C. (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 ...

Strichartz estimates for the Schrödinger equation on a tree and applications

Ignat, L.I. (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 ...

Localized solutions for the finite difference semi-discretization of the wave equation [Solutions localisées pour la semi-discrétisation par différences finies de l'équation des ondes]

Marica, A.; Zuazua, E. (2010-12-31)

We study the propagation properties of the solutions of the finite difference space semi-discrete wave equation on a uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that ...

Localized solutions and filtering mechanisms for the discontinuous Galerkin semi-discretizations of the 1-d wave equation [Solutions localisées et mécanismes de filtrage pour les approximations de Galerkin discontinues de l'équation des ondes.]

Marica, A.; Zuazua, E. (2010-12-31)

We perform a complete Fourier analysis of the semi-discrete 1-d wave equation obtained through a P1 discontinuous Galerkin (DG) approximation of the continuous wave equation on an uniform grid. The resulting system exhibits ...