Related papers: Rough controls for Schroedinger operators on 2-tor…
We prove global internal controllability in large time for the nonlinear Schrodinger equation on a bounded interval with periodic, Dirichlet or Neumann conditions. Our strategy combines stabilization and local controllability near 0. We use…
This paper completely solves the controllability problems of two-dimensional multi-input discrete-time bilinear systems with and without drift. Necessary and sufficient conditions for controllability, which cover the existing results, are…
We continue our study of the reflectionless measures associated to an $s$-dimensional Calder\'{o}n-Zygmund operator (CZO) acting in $\mathbb{R}^d$ with $s\in (0,d)$. Here, our focus will be the study of CZOs that are rigid, in the sense…
This the text of a proceeding accepted for the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014). We present some results of an ongoing research on the controllability problem of an abstract bilinear…
We present here a constructive method of Lagrangian approximate control- lability for the Euler equation. We emphasize on different options that could be used for numerical recipes: either, in the case of a bi-dimensionnal fluid, the use of…
We first show that every operation possesses an unique dual operation and measures an unique effect. If $a$ and $b$ are effects and $J$ is an operation that measures $a$, we define the sequential product of $a$ then $b$ relative to $J$.…
We consider the bilinear Schroedinger equation on a bounded one-dimensional domain and we provide explicit times such that the global exact controllability is verified. In addition, we show how to construct controls for the global…
We investigate trace and observability inequalities for Laplace eigenfunctions on the d-dimensional torus, with respect to arbitrary Borel measures $\mu$. Specifically, we characterize the measures $\mu$ for which the inequalities $$ \int…
We consider the 1D nonlinear Schr\"odinger equation with bilinear control. In the case of Neumann boundary conditions, local exact controllability of this equation near the ground state has been proved by Beauchard and Laurent in…
We study Schroedinger operators with periodic magnetic field in Euclidean 2-space, in the case of irrational magnetic flux. Positive measure Cantor spectrum is generically expected in the presence of an electric potential. We show that,…
We establish the approximate controllability in $L^2$ for the nonlinear Benjamin-Ono equation on torus via two-dimensional control input. Our proof is based on adaptations of geometric control approach introduced by Agrachev and Sarychev.…
We derive in a direct way the exact controllability of the 1D free Schr\"odinger equation with Dirichlet boundary control. We use the so-called flatness approach, which consists in parametrizing the solution and the control by the…
In this paper we establish an almost optimal well-posedness and regularity theory for the Klein-Gordon-Schr\"odinger system on the half line. In particular we prove local-in-time well-posedness for rough initial data in Sobolev spaces of…
In this work we obtain boundedness on weighted variable Lebesgue spaces of some maximal functions that come from the localized analysis considering a critical radius function. This analysis appears naturally in the context of the…
The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp boundsare obtained for both the fractional integral operators and the…
We provide necessary and sufficient geometric conditions for the exact controllability of the one-dimensional fractional free and fractional harmonic Schr\"odinger equations. The necessary and sufficient condition for the exact…
This is the last of a sequence of four papers \cite{param1}, \cite{param2}, \cite{param3}, \cite{param4} dedicated to the construction and the control of a parametrix to the homogeneous wave equation $\square_{\bf g} \phi=0$, where ${\bf…
Since the works of Haraux and Jaffard we know that rectangular plates may be observed by subregions not satisfying the geometrical control condition. We improve these results by observing only on an arbitrarily short segment inside the…
In this paper, we study the local well-posedness of nonlinear Schr\"odinger equations on tori $\mathbb{T}^{d}$ at the critical regularity. We focus on cases where the nonlinearity $|u|^{a}u$ is non-algebraic with small $a>0$. We prove the…
We investigate the relationship between measurable differentiable structures on doubling metric measure spaces and derivations. We prove: [1] a decomposition theorem for the module of derivations into free modules; [2] the existence of a…