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.

Smoothness of the density for solutions to Gaussian rough differential equations

Abstract: We consider stochastic differential equations driven by a multi-dimensional Gaussian process. Under the assumption that the vector fields satisfy Hormander's bracket condition, we demonstrate that the solution admits a smooth density for any strictly positive time t, provided the driving noise satisfies certain non-degeneracy assumptions. Our analysis relies on an interplay of rough path theory, Malliavin calculus, and the theory of Gaussian processes. Our result applies to a broad range of examples including fractional Brownian motion with Hurst parameter greater than 1/4, the Ornstein-Uhlenbeck process and the Brownian bridge returning after time T.

Artificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations

Abstract: This paper addresses the construction of nonlinear integro-differential artificial boundary conditions for one-dimensional nonlinear cubic Schrodinger equations. Several ways of designing such conditions are provided and a theoretical classification of their accuracy is given. Semidiscrete time schemes based on the method developed by Duran and Sanz-Serna [IMA J. Numer. Anal. 20 (2000), pp. 235-261] are derived for these unusual boundary conditions. Stability results are stated and several numerical tests are performed to analyze the capacity of the proposed approach.

Null controllability of the structurally damped wave equation with moving control

Abstract: We investigate the internal controllability of the wave equation with structural damping on the one-dimensional torus. We assume that the control is acting on a moving point or on a moving small interval with a constant velocity. We prove that the null controllability holds in some suitable Sobolev space and after a fixed positive time independent of the initial conditions.

Nombres premiers de la forme⌊n c ⌋

Abstract: For we denote by the number of integers such that is prime. In 1953, Piatetski-Shapiro has proved that holds for . Many authors have extended this range, which measures our progress in exponential sums techniques. In this article we obtain .

Choix des signes pour la formalité de M. Kontsevich

Abstract: The explicit realization of M. Kontsevich\'s formality on $R^d$ is the main step of the proof of formality theorem on any manifold. We present here a coherent choice of orientations and signs in order to write completely M. Kontsevich\'s proof for $R^d$, including all the signs appearing in the formality equation.