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On considère l’équation des ondes sur un rectangle avec un feedback de type Dirichlet. On se place dans le cas où la condition de contrôle géométrique n’est pas satisfaite (BLR Condition), ce qui implique qu’on n’a pas stabilité exponentielle dans l’espace d’énérgie. On prouve qu’on peut trouver un sous espace de l’espace d’énergie tel qu’on a stabilité exponentielle. De plus, on montre un résultat de décroissance polynomiale pour toute donnée initiale régulière.
On s'intéresse dans cet article, a la stabilisation de l'équation des ondes dans un domaine extérieur avec condition de Dirichlet...
A powerfull method has been developped in [2] for the study of -stability of travelling waves in conservation laws or more generally in equations which display -contractivity, maximum principle and mass conservation. We recall shortly the general procedure. We also show that it partly applies to the waves of a model of radiating gas. These waves have first been studied by Kawashima and Nishibata [5,6] in a different framework. Therefore, shock fronts for this model are stable under mild perturbations....
We consider here the Interior Penalty Discontinuous Galerkin (IPDG) discretization of the wave equation. We show how to derive the optimal penalization parameter involved in this method in the case of regular meshes. Moreover, we provide necessary stability conditions of the global scheme when IPDG is coupled with the classical Leap–Frog scheme for the time discretization. Numerical experiments illustrate the fact that these conditions are also sufficient.
We consider a generalized 1-D von Foerster equation. We present two discretization methods for the initial value problem and study stability of finite difference schemes on regular meshes.
In this paper we study the stability of transonic strong shock solutions of the steady state one-dimensional unipolar hydrodynamic model for semiconductors in the isentropic case. The approach is based on the construction of a pseudo-local symmetrizer and on the paradifferential calculus with parameters, which combines the work of Bony-Meyer and the introduction of a large parameter.
This article investigates the long-time behaviour of parabolic scalar conservation laws of the type , where and the flux is periodic in . More
specifically, we consider the case when the initial data is an disturbance of a stationary periodic solution. We show, under polynomial growth assumptions on the flux, that the difference between u
and the stationary solution behaves in norm like a self-similar profile for large times. The proof uses a time and space change of variables which is...
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