Institution
Institut Élie Cartan de Lorraine
Facility•Vandœuvre-lès-Nancy, France•
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.
Topics: Boundary value problem, Stochastic differential equation, Boundary (topology), Brownian motion, Nonlinear system
Papers published on a yearly basis
Papers
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TL;DR: In this paper, the authors consider the one-dimensional nonlinear Schrodinger equation with a nonlinearity of degree p>1 and show that the nonlinear evolution is continuous with respect to the linear Schrodinger flow.
Abstract: We consider the one-dimensional nonlinear Schrodinger equation with a nonlinearity of degree $p>1$. We exhibit measures on the space of initial data for which we describe the non trivial evolution by the linear Schr\"odinger flow and we show that their nonlinear evolution is absolutely continuous with respect to this linear evolution. We deduce from this precise description the global well-posedness of the equation for $p>1$ and scattering for $p>3$. To the best of our knowledge, it is the first occurence where the description of quasi-invariant measures allows to get quantitative asymptotics (here scattering properties) for the nonlinear evolution.
10 citations
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TL;DR: In this paper, the authors considered the classical Wiener-Ikehara Tauberian theorem with a generalized condition of slow decrease and some additional poles on the boundary of convergence of the Laplace transform.
Abstract: We consider the classical Wiener–Ikehara Tauberian theorem, with a generalized condition of slow decrease and some additional poles on the boundary of convergence of the Laplace transform. In this generality, we prove the otherwise known asymptotic evaluation of the transformed function, when the usual conditions of the Wiener-Ikehara theorem hold. However, our version also provides an effective error term, not known thus far in this generality. The crux of the proof is a proper asymptotic variation of the lemmas of Ganelius and Tenenbaum, also constructed for the sake of an effective version of the Wiener–Ikehara theorem.
10 citations
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TL;DR: A bi-scale model describing the cell and tumor lifespans by random variables is proposed and a ROC curve, entitled ECT (Efficiency-Complication Trade-off), suited to the selection by clinicians of the appropriate treatment planning is proposed.
10 citations
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TL;DR: It is proved that measurable flows exist under weak conditions, even solutions to the corresponding rough differential equations are not unique, and it is shown that under additional conditions of the approximation, there exists a unique Lipschitz flow.
Abstract: We introduce a new framework to deal with rough differential equations based on flows and their approximations. Our main result is to prove that measurable flows exist under weak conditions, even solutions to the corresponding rough differential equations are not unique. We show that under additional conditions of the approximation, there exists a unique Lipschitz flow. Then, a perturbation formula is given. Finally, we link our approach to the additive, multiplicative sewing lemmas and the rough Euler scheme.
10 citations
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TL;DR: In this article, a system of Korteweg-de Vries equations posed on an oriented tree-shaped network was successfully controlled with less inputs than equations, and the couplings and the controls appeared only on boundary conditions.
Abstract: Controllability of coupled systems is a complex issue depending on the coupling conditions and the equations themselves. Roughly speaking, the main challenge is controlling a system with less inputs than equations. In this paper this is successfully done for a system of Korteweg-de Vries equations posed on an oriented tree shaped network. The couplings and the controls appear only on boundary conditions.
10 citations
Authors
Showing all 361 results
Name | H-index | Papers | Citations |
---|---|---|---|
Ivan Nourdin | 44 | 217 | 6139 |
Marius Tucsnak | 33 | 114 | 3907 |
Victor Nistor | 31 | 158 | 3352 |
Xavier Antoine | 30 | 125 | 2992 |
Jan Sokołowski | 30 | 203 | 6056 |
Nicolas Fournier | 29 | 106 | 3044 |
Gérald Tenenbaum | 29 | 173 | 5100 |
Lionel Rosier | 29 | 126 | 3956 |
Vicente Cortés | 27 | 118 | 2356 |
Gauthier Sallet | 27 | 70 | 2007 |
Antoine Henrot | 26 | 128 | 3268 |
Samy Tindel | 26 | 168 | 2656 |
Bruno Scherrer | 25 | 69 | 1447 |
Mario Sigalotti | 25 | 180 | 2082 |
Takéo Takahashi | 24 | 87 | 1673 |