Stabilisation frontière indirecte de systèmes faiblement couplés

This work is concerned with the boundary stabilization of coupled equations where only one of the equation is stabilized (indirect damping, see e.g. Russell [9]). We show for different examples (wave equations, Kirchhoff plates) that the full system can be strongly stabilized by that way, provided that the coupling parameter is sufficiently small (but not equal to zero). In such cases we prove that the energy decays polynomially with explicit polynomial decay rates for sufficiently smooth solutions. We extend these results to the case of two coupled wave equations with different speeds of propagation under a condition of the ratio of the two speeds and for n-dimensional intervals.     

Problèmes aux limites non homogènes (VI)

Sans résumé Les résultats de ce travail ont été annoncés au Congrès International de Stockholm (ao?t 1962).     

Problèmes aux limites non homogènes (VII)

Annali di Matematica Pura ed Applicata (1923 -) -     

Ouverts convexes homogènes des espaces affines

Sans résumé     

Approximation du système quasigéostrophique à l'aide des systèmes primitifs

In this paper we show that the quasigeostrophic system is well approximated by the primitive systems. More precisely, we prove that if the initial data are well-prepared, then the maximal time existence of the regular solution of the primitive system goes to infinity and the regular solution goes to the solution of the quasigeostrophic system, strongly on an arbitrary time interval. By “well-prepared initial data” we mean that the initial data of the primitive systems is converging to an initial data with zero oscillating part.     

Stabilisation frontière d'un système d'élasticité

We prove in this Note the global existence, uniqueness and stabilization of an elasticity system with nonlinear boundary damping. This work extends results obtained by Alabau and Komornik in [1]     

Espaces homogènes génériquement triviaux

We study the homogeneous spaces of a smooth group G over affine spaces or local k-algebra and gerbs locally banded by a semi-simple group H dèfine over k. In particular we show that every gerb locally banded by H and rationally trivial is trivial, and that an homogeneous space of G with semi-simple isotropy which is rationally trivial is trivial in the Zariski topology. This extends a result of Colliot-Thélène and Ojanguren concerning G-torsors.