Stabilisation frontière de problèmes de Ventcel

We study Ventcel's problems for the wave equation and the isotropic linear elastodynamic system. The boundary observability and the exact controlabillity were established in [3]. We prove the energy decay for the elastodynamic system with stationary Ventcel's conditions. We also give a boundary feedback leading to arbitrarily large energy decay rates for the elastodynamic system with evolutive Ventcel's conditions. A spectral study proves, finally, that the “natural” feedback is not sufficient for the exponential decay in the case of the wave equation with Ventcel's conditions.     

Complète intégrabilité singulière

We show that an holomorphic vector field in a neighbourhood of its singular point 0 0 ∈ ℂⁿ is analytically normalizable as soon as it has a sufficiently large number of commuting holomorphic vector fields, a sufficiently large number of formal first integrals, and that a Diophantian small divisors condition related to its linear part is satisfied.     

Algèbre Pré-Gerstenhaber à homotopie près

This paper is concerned by the concept of algebra up to homotopy for a structure defined by two operations . and $[,]$. An important example of such a structure is the Gerstenhaber algebra (i.e. commutatitve structure with degree 0 and Lie structure with degree ?1). The notion of Gerstenhaber algebra up to homotopy ($G_{\infty }$ algebra) is known: it is a codifferential bicogebra.Here, we give a definition of pre-Gerstenhaber algebra (pre-commutative and pre-Lie) allowing a similar construction for a $\text{pre}{G}_{\infty }$ algebra.Given a structure of pre-commutative (Zinbiel) and pre-Lie algebra and working over the corresponding Koszul dual operads, we will give an explicit construction of the associated pre-Gerstenhaber algebra up to homotopy: it is a bicogebra (Leibniz and permutative) equipped with a codifferential which is a coderivation for the two coproducts.     

Stabilisation des systèmes bilinéaires homogènes

We deal with the problem of stabilizing the bilinear homogeneous systems. We give sufficient conditions for a bilinear system to be stabilizable with homogeneous feedback of degree zero. The explicit design of the feedback is given.     

关于Cauchy-Fantappiè公式

<正> §1.前言与符号多复变数函数论中有许多种形式的 Cauchy 公式,关于这方面有丰富的文献,从 F.Norguet 的文章之附录中可见一斑.他把重要者分为三种类型,其一我们称之为 A.Weil的 Cauchy 公式(例如见[2]),其一称之为 S.Bochner与 E.Martinelli 的 Cauchy 公式(例如见[3]与[4]),其一称之为典型域(即非例外的有界对称域)的 Cauchy 公式(例如见S.Bochner[5]与华罗庚[6]).但是,一个复变数函数论中只有一种 Cauchy 公式,自然     

Algèbres localement uniformémentA-pseudo-convexes advertiblement complètes

We examine the structure and the spectral properties of locally uniformlyA-pseudo-convex algebras.      

Algorithmes parallèles asynchrones pour des systèmes singuliers

In this paper we give a convergence result concerning parallel bounded delayed asynchronous algorithms for linear fixed point problems with nonexpansive linear mappings with respect to a weighted maximum norm. This allows us to propose parallel algorithms which converge to the solution of consistent singular systems, including singular M-matrices (see for more details [3]). An important characteristic of our technical framework is that we are able to describe two-stage algorithms.     

Modèles semi-factoriels et modèles de Néron

Let S be the spectrum of a discrete valuation ring with function field K. Let X be a scheme over S. We will say that X is semi-factorial over S if any invertible sheaf on the generic fiber X _K can be extended to an invertible sheaf on X. Here we show that any proper geometrically normal scheme over K admits a proper, flat, normal and semi-factorial model over S. We also construct some semi-factorial compactifications of regular S-schemes, such as Néron models of abelian varieties. The semi-factoriality property for a scheme X/S corresponds to the Néron property of its Picard functor. In particular, one can recover the Néron model of the Picard variety ${{\rm Pic}_{X_K/K,{\rm red}}^0}$ of X _K from the Picard functor Pic _X/S , as in the known case of curves. This provides some information on the relative algebraic equivalence on the S-scheme X.     

Problèmes de Monge-Ampère, courbes holomorphes et laminations

Riemann's Uniformization theorem is a classical tool for the study of elliptic problems on surfaces. Usually, the use of this theorem reflects the fact that the situation can be translated in a pseudo-holomorphic language: the solutions of the problem appearing as holomorphic curves for a suitable almost complex structure in a jet space. Often, the lack of compactness of the space of solutions of bounded energy is remarkably described by Gromov's compactness theorem on holomorphic curves. On the other hand for other problems, usually related to Monge-Ampère equations, a different type of lack of compactness appears; solutions with bounded energy converge and, furthermore, it is possible to describe what happens when the energy goes to infinity: the solutions tend to degenerate along holomorphic curves described by solutions of ODE. The goal of this article is to describe the "Monge-Ampère geometry" of the jet-space that corresponds to this phenonemon. We prove compactness results for the solutions of these problems, and show examples and applications of our technique. Furthermore, a moduli space of pointed solutions is exhibited with its structure of a riemaniann lamination. Submitted: December 1995, revised version: September 1996, final version: March 1997     

Systèmes fortement hyperboliques et systèmes symétriques

a is a matrix valued 4 × 4 strongly hyperbolic operator; we state the following result: if the reduced dimension of a is superior or equal to 8, a is symmetric in a convenient basis.     

Problèmes aux limites non homogènes (VII)

Annali di Matematica Pura ed Applicata (1923 -) -     

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]     

Un Théorème sur les Espaces homogènes complexes

Sans résuméDédié à M. lc Prof.Alexandre Ostrowski     

Corps biquadratiques monogènes

Let be a biquadratic number field (where d,m,n∈ℤ, are uniquely determined); we say that it is monogenic if its ring of integers O_K is of the form ℤ[θ]. We show that K is monogenic if and only if the two following conditions are satisfied:

Quaternionic Monge-Ampère equations

The main result of this article is the existence and uniqueness of the solution of the Dirichlet problem for quaternionic Monge-Ampère equations in quaternionic strictly pseudoconvex bounded domains in ℍ ⁿ . We continue the study of the theory of plurisubharmonic functions of quaternionic variables started by the author at [2].     

Solutions régulières du problème de Riemann bidimensionnel

We introduce a notion of characteristic codirections for 2 × 2 systems of conservation laws in two-dimensional space. These codirections are used to construct rarefaction waves.     

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.     

Caractère bien posé du problème de Cauchy pour le système de Bérenger

The Bérenger perfectly matched layer is used in computational electromagnetism as an absorbing layer in scattering problems. It raises delicate mathematical issues. In this Note we show, for regular data, the existence and uniqueness of strong solutions to the Cauchy problem derived from the PML method. The result is presented in the 2-D case. The key to the proof is an appropriate control of a mixed H¹- L² norm of the solution by the same norm of the initial data. Beside a paper is in preparation about extensions of this results (L² estimates, 3-D case) (see also [5]).