Institut Élie Cartan de Lorraine

About: Institut Élie Cartan de Lorraine is a facility organization based out in Vandœuvre-lès-Nancy, France. It is known for research contribution in the topics: Boundary value problem & Stochastic differential equation. The organization has 345 authors who have published 1084 publications receiving 15512 citations. The organization is also known as: Institut Élie-Cartan de Nancy.

On the stability of Timoshenko-type systems with internal frictional dampings and discrete time delays

Abstract: In this paper, we consider a vibrating system of Timoshenko-type in a bounded one-dimensional domain under Dirichlet-Dirichlet or Dirichlet-Neumann boundary conditions with one or two discrete time delays and one or two internal frictional dampings. First, we show that the system is well posed in the sens of semigroup theory. Second, we prove the exponential stability regardless to the speeds of wave propagation of the system if the weights of the time delays are smaller than the ones of the corresponding dampings, respectively. However, when the weight of one time delay is not smaller than the one of the corresponding damping, we prove the exponential stability in case of equal-speed wave propagation, and the polynomial stability in the opposite case.

Sur certaines singularités non isolées d’hypersurfaces I

Abstract: L'objectif de cet article est de mettre en place, dans le cadre de fonctions a lieu singulier de dimension 1, avec des hypotheses assez restrictives mais donnant acces a beaucoup d'exemples non triviaux, l'analogue de la theorie de E. Brieskorn pour une fonction a singularite isolee. Les principaux resultats sont le theoreme de finitude pour le (a, b)-module associe a l'origine, qui est obtenu via le theoreme de constructibilite de M. Kashiwara, et les resultats de non torsion pour une courbe plane (non necessairement reduite) et pour la suspension d'un tel cas sans torsion avec une singularite isolee.

Macdonald's formula for Kac-Moody groups over local fields

Abstract: For an almost split Kac-Moody group G over a local non-archimedean field, the last two authors constructed a spherical Hecke algebra H (over the complex numbers C, say) and its Satake isomorphism with the commutative algebra of Weyl invariant elements in some formal series algebra C[[Y]].In this article, we prove a Macdonald's formula, i.e. an explicit formula for the image of a basis element of H. The proof involves geometric arguments in the masure associated to G and algebraic tools, including the Cherednik's representation of the Bernstein-Lusztig-Hecke algebra (introduced in a previous article) and the Cherednik's identity between some symmetrizers.

Mathematical Analysis for a model of Nickel-Iron alloy electrodeposition on rotating disk electrode: parabolic case

Abstract: To better understand the nickel-iron electrodeposition process, we are interested in the one-dimensional model. This model addresses dissociation, diffusion, electromigration, convection and deposition of multiple ion species. We study the global existence of solutions that are here different ion concentrations in the mixture as well as the electric potential. The non regularity of data imposes us to introduce the notion of weak solution adapted for our model. The classic techniques, based on the C estimations, to prove the existence and the positivity of solutions fall in defect and news techniques must be developed. We present them here and we obtain global existence and positivity of weak solution for our model without no restriction of growth on the non linear terms.

On the time evolution of Bernstein processes associated with a class of parabolic equations

Abstract: In this article dedicated to the memory of Igor D. Chueshov, I first summarize in a few words the joint results that we obtained over a period of six years regarding the long-time behavior of solutions to a class of semilinear stochastic parabolic partial differential equations. Then, as the beautiful interplay between partial differential equations and probability theory always was close to Igor's heart, I present some new results concerning the time evolution of certain Markovian Bernstein processes naturally associated with a class of deterministic linear parabolic partial differential equations. Particular instances of such processes are certain conditioned Ornstein-Uhlenbeck processes, generalizations of Bernstein bridges and Bernstein loops, whose laws may evolve in space in a non trivial way. Specifically, I examine in detail the time development of the probability of finding such processes within two-dimensional geometric shapes exhibiting spherical symmetry. I also define a Faedo-Galerkin scheme whose ultimate goal is to allow approximate computations with controlled error terms of the various probability distributions involved.