Éditeur(s) : Université des Antilles
Description : En 2018, l'Université des Antilles honorait 62 docteurs issus des promotions 2016 et 2017 des deux écoles doctorales E588 et E589. La cérémonie de remise des diplômes, célébrant la fin d'une aventure scientifique, intellectuelle et humaine, a réuni 19 docteurs pour le pôle Guadeloupe.

Droits : CC-BY-NC-ND - Attribution - Pas d'utilisation commerciale - Pas de modification
Permalien : http://www.manioc.org/fichiers/V18225
V18225

Éditeur(s) : HAL CCSD AIMS Press
Résumé : International audience
In this article, we obtain sucient conditions to obtain finite time blowup in a system of two coupled nonlinear Schrödinger (NLS) equations in the critical case. This system mainly considered here in dimension 2, couples one equation including gain and the other one including losses, constituting a generalization of the model of pulse propagation in birefringent optical fibers. In the spirit of the seminal work of Glassey, the proofs used the virial technique arguments.
ISSN: 2473-6988

hal-01492062
https://hal.univ-antilles.fr/hal-01492062
DOI : 10.3934/Math.2017.1.195

Éditeur(s) : HAL CCSD Juliusz Schauder University Centre for Nonlinear Studies
Résumé : International audience
ISSN: 1230-3429

hal-01545552
https://hal.archives-ouvertes.fr/hal-01545552
DOI : 10.12775/TMNA.1999.016

Éditeur(s) : HAL CCSD
Résumé : To appear in TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS (16 pages).
In the last two decades, many algebras of generalized functions have been constructed, particularly the so-called generalized Sobolev algebras. Our goal is to study the latter and some of their main properties. In this framework, we pose and solve a nonlinear degenerated Dirichlet problem with irregular data such as Dirac generalized functions.
https://hal.archives-ouvertes.fr/hal-00004903

Droits : info:eu-repo/semantics/OpenAccess
hal-00004903
https://hal.archives-ouvertes.fr/hal-00004903
https://hal.archives-ouvertes.fr/hal-00004903/document
https://hal.archives-ouvertes.fr/hal-00004903/file/sb_psn_pjm.pdf
ARXIV : math.GM/0505228

Éditeur(s) : HAL CCSD Université Paul Sabatier _ Cellule Mathdoc
Résumé : International audience
ISSN: 0240-2963

hal-01545674
https://hal.archives-ouvertes.fr/hal-01545674

Éditeur(s) : HAL CCSD Tsing Hua University
Résumé : International audience
ISSN: 1607-2510

hal-01312455
https://hal.archives-ouvertes.fr/hal-01312455

Éditeur(s) : HAL CCSD Wiley-Blackwell
Résumé : International audience
We mainly study a system of two coupled nonlinear Schrödinger equations where one equation includes gain and the other one includes losses. This model constitutes a generalization of the model of pulse propagation in bire-fringent optical fibers. We answered partially to a question of some authors in [8], that in the Manakov case, the solution stays in L 2 (0, T ; H 1), that means that the solution can not blow up in finite time. More precisely, the bound that is provided in this paper does not seem to be optimal but different than those that has been given from a previous study [8]. Thanks to the way we treat the a priori estimate, we obtain a sharp bound in L 2 (0, T ; H 1), which would be difficult to reach from the study of other authors [8]. The result is illustrated by numerical results which have been obtained with a finite element solver well adapted for that purpose.
ISSN: 0022-2526

Droits : http://creativecommons.org/licenses/by/
hal-01270459
https://hal.archives-ouvertes.fr/hal-01270459
https://hal.archives-ouvertes.fr/hal-01270459/document
https://hal.archives-ouvertes.fr/hal-01270459/file/paperver2.pdf