La résolution du problème de Cauchy pour un système d'équations du second ordre par la méthode de Riemann

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Les demi-surfaces de Riemann. Application au problème du type

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Existence de solutions d'un problème de couplage fluide-structure bidimensionnel instationnaire

We study the well-posedness of a steady stale problem: we consider a two-dimensional viscous incompressible flow, which is modeled bv the Navier-Stokes equations. The structure is a rigid moving disc. The fluid domain depends on time and is defined by the position of the structure, itself resulting from a stress distribution coming from the fluid. The problem is then nonlinear and the equations we deal with are coupled. We prove its local solvability in time though two fixed point procedures.     

Sur la monodromie du problème de Cauchy ramifié

In this paper, we study the monodromy of the ramified Cauchy problem for operators with multiple characteristics of constant multiplicity. More precisely, we give an estimation of the eigenvalues of the solution's monodromy, first with the assumptions of the theorem of Hamada–Leray–Wagschal, then with the assumptions of the theorem of Leichtnam.     

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 la généralisation du problème de Dirichlet

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Sur la généralisation du problème de Dirichlet

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Une généralisation du problème des itérés

For given systems of differential operators of constant coefficients we give algebraic conditions to compare their spaces of Gevrey vectors.     

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]).     

Les espaces réguliers et le problème de métrisation

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Existence et unicité de solutions d'un problème de couplage fluide-structure bidimensionnel stationnaire

We study the well-posedness of a steady-state problem: we consider a two-dimensional viscous incompressible flow, which is modeled by the Stokes equations. The structure is monodimensional and the equations describing the behaviour of elastic medium are beam equations. The fluid domain is defined by the shape of the structure function, itself resulting from a stress distribution coming from the fluid. The problem is thus nonlinear and the equations we deal with are coupled. We prove its solvability through Schauder's fixed point theorem.     

Sur un problème de Rényi

Let (n) be the number of all prime divisors ofn and (n) the number of distinct prime divisors ofn. We definev _q (x)=|{nx(n)–(n)=q}|. In this paper, we give an asymptotic development ofv _q (x); this improves on previous results.

     

Sur l’ordre de grandeur des quotients partiels du développement en fractions continues régulières

 For any irrational , let denote the regular continued fraction expansion of x and define f, for all z > 0 by and by J. GALAMBOS proved that (μ the Gauss measure)

Sur l’ordre de grandeur des quotients partiels du développement en fractions continues régulières

 For any irrational , let denote the regular continued fraction expansion of x and define f, for all z > 0 by and by J. GALAMBOS proved that (μ the Gauss measure)