Modèles linéaires généralisés fonctionnels avec dérivée

We consider the functional generalized linear model whose response function is a linear operator depending on an explanatory variable X belonging to a functional space. It has been studied, among others, by Cardot and Sarda [4]. In this paper, we consider the functional generalized linear model with derivative component, denoted MLGFD in the following, whose response function depends on a linear operator of X and on its derivative. We propose estimators for the unknown functional parameters and provide convergence rates.     

Un problème de convection-diffusion avec réaction chimique

The purpose of this Note is to study the dynamic of a problem of mass and heat transfer in the presence of a chemical reaction.     

Sur certains problèmes elliptiques asymétriques avec poids indéfinis

We prove the existence of a first nontrivial eigenvalue for the problem (1.2) below. As applications we study the solvability of (1.1) below as well as the Fučik spectrum with weights for the p-Laplacien.     

Théorème de division avec des conditions au bord

Let be an open subset of ⁿ and be a subalgebra of the algebra of analytic functions on . We suppose that satisfies some weak conditions of noetherianity such that we can construct a finite stratification for each ideal of . We also suppose that satifies global £ojasiewicz's inequalities. We prove the following: Let andf C on flat on ; if for eacha the Taylor's serie off ata, T _a f, is in the ideal generated byT _a f ₁,...,T _a f _p in the ring of formal power series, then there exist ₁,..., _p ,C on flat on such that . This result extends the classic Hormander's theorem of division (for a polynomial) or the £ojasiewicz-Malgrange theorem in the local analytic case.Reherches menées dans le cadre du Programme d'Appui à la Recherche Scientifique (PARS MI 33)     

Étude d'un système avec température dans les semi-conducteurs

The aim of this Note is to study a system of partial differential equations arising in semiconductors. We prove an existence of variational solution using Schauder's fixed point theorem. If the domain is narrow in one direction, we also prove a uniqueness result.     

Dynamique d'un modèle intégro-différentiel de flamme sphérique avec pertes de chaleur

We present the mathematical study of a model of spherical flames, described by a singular integro-differential equation; we are interested here in the asymptotic behaviour of these flames which ignite or stabilize towards critical radiuses, depending on heat losses and the energy input.     

Modélisation d'un problème de diffusion avec pyrolyse et ablation

We discuss existence and uniqueness for the solutions of an unusual parabolic quasilinear problem, coming from a heat conduction model problem (atmosphere re-entry of a body) with pyrolysis and weak ablation.     

Un modèle homogénéisé pour les marches aléatoires avec états internes

We study the asymptotic behavior of random walks with internal states. We show that under suitable conditions the limit behavior of random walks is described by a certain system of partial differential equations. It turns out that for arbitrary initial conditions, certain internal states have equal probabilities in the asymptotic regime.     

Stabilisation frontière de plaques de Kirchhoff avec résolvante non compacte

Using a direct approach, we prove the asymptotic stability of Kirchhoff plates in the absence of compactness of the resolvent. We also establish the polynomial energy decay rate for the smooth solutions.     

Existence de solutions pour le modèle dérive-diffusion avec terme d'avalanche

The aim of this Note is the study of a system of partial differential equations arising in semiconductors in the presence of the avalanche term and nonconstant mobilities. We prove an existence of variational solution using Schauder's fixed point theorem.     

Contrôlabilité exacte d'un problème avec conditions de Ventcel évolutives pour le système linéaire de l'élasticité

We examine the exact controllability of the solution of the linear elasticity system with evolutive Ventcel conditions in a bounded domain of ø³. We use the Hubert uniqueness method (HUM) of Lions [7]; some multipliers are defined on the boundary: the curvature tensor [3] appears when computing some boundary integrals.     

Éléments finis non conformes pour un problème de contact unilatéral avec frottement

In a previous study, we considered it nonconforming finite element method for a frictionless contact problem. The aim of this note is to establish the convergence of the method for a frictional contact problem between two deformable bodies.     

Problèmes elliptiques avec non-linéarité discontinue et second membre L1

We define the notion of (very) weak solution for a class of semilinear elliptic problems with discontinuous nonlinearity and L¹ data. We prove the existence of such a solution by an approximation technique with L² datas.     

Solutions périodiques d'un système différentiel non linéaire du second ordre avec changement de signe

Résumé On s'intéresse à la recherche de solutions T périodiques d'un système + a(t)V(x)= =f(t), où a:R R et f:R Rⁿ sont T périodiques. Le potentiel V est supposé convexe sous quadratique et on utilise la formulation variationnelle duale du problème. On démontre différents résultats d'existence d'au moins une solution au problème, non triviale dans le cas où la fonction f est nulle.     

Approximation du problème de contact unilatéral par la méthode des éléments finis avec joints

The purpose of this Note is to extend the mortar finite element method to handle the unilateral contact model between two deformable bodies. The corresponding variational inequality is approximated using finite elements with meshes which do not fit on the contact zone. The mortar technique allows us to match (independent) discretizations within each solid and to express the contact conditions in a satisfying way. Then, we carry out a numerical analysis of the algorithm and, using a bootstrap argument, we give an upper bound of the convergence rate similar to that already obtained for compatible grids.     

Un théorème de Liouville pour l'opérateur de Schrödinger avec dérive

Let $(M,g)$ be a complete Riemannian manifold without boundary of dimension n and V be a $C^2$ vector field on M such that $r(x)|V(x)|$ is bounded. Suppose that ${\mathrm{Ric}}_g(x)??\min \{\lambda (r(x))?{\mu }_{\mathrm{?}V}(x),\beta (r(x))\}$ outside a compact set of M, where ${\mu }_{\mathrm{?}V}$ denotes the upper eigenvalue of ?V and $\lambda ,\beta$ are non-negative decreasing functions such that ${\lim }_{t\to +\infty }{t}^2\lambda (t)=0$. There exists positive numbers $b_n$ and $c_n$ which depend only on n and $6V{6}_{\infty }$ such that if h is a $C^2$ function defined on M with $\mathrm{\Delta }h??c_n{a}^2$ and ${\mathrm{lim?sup}}_{R\to \infty }{R}^{\mathrm{?2}}{\min }_{x\in B_p(3R)?B_p(R)}h(x)??b_n{a}^2$, where $0?a<{\mathrm{lim?inf}}_{j\to \infty }h(z_j)$, where $(z_j)$ is a sequence of M such that $r(z_j)\to \infty$, then the equation $\mathrm{\Delta }u(x)+V(x)?\mathrm{?}u(x)+h(x)u(x)=0$ has no positive $C^2$ solution on M. To cite this article: S. Asserda, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Etude d'un système stationnaire linéarisé d'équations primitives avec des termes de pression additionnels

We consider a linearized system of primitive equations for the ocean in the steady-state case with additional terms of pressure. First, we first motivate the introduction of these additional terms of pressure, and then we interpret them. Finally, we state an existence and uniqueness result for the considered system.