Eigenfunction Expansions and the Pinksy Phenomenon on Compact Manifolds.
Ein nichtlinearer Interpolationssatz und seine Anwendung auf nichtlineare Wellengleichungen.
Einige Eigenschaften der Lösung der Wellengleichung mit der Korrektion von Rayleigh
Elastic wave propagation in parallel: the Huygens' approach.
The use of parallel computers makes it feasible to simulate elastic waves throughout large heterogeneous structures, and new domain decomposition methods can be used to increase their efficiency and decrease the computing time spent in the simulation. In this paper we introduce a simple parallel algorithm for the propagation of elastic waves in complex heterogeneous media after a finite element discretization. This method performs more efficiently than classic domain decomposition techniques based...
Energy estimate for wave equations with coefficients in some Besov type class.
Enlarged Asymptotic Compensation in Discrete Distributed Systems
This work concerns an enlarged analysis of the problem of asymptotic compensation for a class of discrete linear distributed systems. We study the possibility of asymptotic compensation of a disturbance by bringing asymptotically the observation in a given tolerance zone 𝒞. Under convenient hypothesis, we show the existence and the unicity of the optimal control ensuring this compensation and we give its characterization
Équation des ondes amorties dans un domaine extérieur
On étudie la position des pôles de diffusion du problème de Dirichlet pour l’équation des ondes amorties du type dans un domaine extérieur. Sous la condition du « contrôle géométrique extérieur », on déduit alors le comportement des solutions en grand temps. On calcule en particulier le meilleur taux de décroissance de l’énergie locale en dimension impaire d’espace.
Équations d'évolution avec non linéarité logarithmique
Equilibrium points for a wave equation with boundary control containing an integral term. (Points d'équilibre pour une équation des ondes avec contrôle frontière contenant un terme intégral.)
Error estimates for Galerkin reduced-order models of the semi-discrete wave equation
Galerkin reduced-order models for the semi-discrete wave equation, that preserve the second-order structure, are studied. Error bounds for the full state variables are derived in the continuous setting (when the whole trajectory is known) and in the discrete setting when the Newmark average-acceleration scheme is used on the second-order semi-discrete equation. When the approximating subspace is constructed using the proper orthogonal decomposition, the error estimates are proportional to the sums...
Estimates for the cut-off resolvent of the Laplacian for trapping obstacles
Estimation Lp de la solution de l'equation des ondes sur le demi-plan de Poincaré.
Estimations de Strichartz généralisées sur le groupe de Heisenberg
Étude numérique des pôles de résonance associés à la diffraction d'ondes acoustiques et élastiques par un obstacle en dimension 2
Exact controllability for semilinear wave equations in one space dimension
Exact controllability for temporally wave equation.
Exact controllability in fluid – solid structure: The Helmholtz model
A model representing the vibrations of a fluid-solid coupled structure is considered. Following Hilbert Uniqueness Method (HUM) introduced by Lions, we establish exact controllability results for this model with an internal control in the fluid part and there is no control in the solid part. Novel features which arise because of the coupling are pointed out. It is a source of difficulty in the proof of observability inequalities, definition of weak solutions and the proof of controllability...
Exact controllability in fluid–solid structure : the Helmholtz model
A model representing the vibrations of a fluid-solid coupled structure is considered. Following Hilbert Uniqueness Method (HUM) introduced by Lions, we establish exact controllability results for this model with an internal control in the fluid part and there is no control in the solid part. Novel features which arise because of the coupling are pointed out. It is a source of difficulty in the proof of observability inequalities, definition of weak solutions and the proof of controllability results....
Exact controllability in short time for the wave equation
Exact controllability of the 1-d wave equation from a moving interior point
We consider the linear wave equation with Dirichlet boundary conditions in a bounded interval, and with a control acting on a moving point. We give sufficient conditions on the trajectory of the control in order to have the exact controllability property.