| dc.contributor.author | Ekeland, Ivar | * |
| dc.contributor.author | Séré, Eric | * |
| dc.date.accessioned | 2020-04-28T12:50:29Z | |
| dc.date.available | 2020-04-28T12:50:29Z | |
| dc.date.issued | 2020 | |
| dc.identifier.uri | https://basepub.dauphine.fr/handle/123456789/20668 | |
| dc.language.iso | en | en |
| dc.subject | nonlinear Schrodinger system | |
| dc.subject | Ekeland's variational principle | |
| dc.subject | Cauchy problem | |
| dc.subject | Nash-Moser theorem | |
| dc.subject | Inverse function theorem | |
| dc.subject | loss of derivatives | |
| dc.subject | singular perturbations | |
| dc.subject.ddc | 510 | en |
| dc.title | A surjection theorem for maps with singular perturbation and loss of derivatives | |
| dc.type | Document de travail / Working paper | |
| dc.description.abstracten | In this paper we introduce a new algorithm for solving perturbed nonlinear functional equations which admit a right-invertible linearization, but with an inverse that loses derivatives and may blow up when the perturbation parameter ϵ goes to zero. These equations are of the form Fϵ(u)=v with Fϵ(0)=0, v small and given, u small and unknown. The main difference with the by now classical Nash-Moser algorithm is that, instead of using a regularized Newton scheme, we solve a sequence of Galerkin problems thanks to a topological argument. As a consequence, in our estimates there are no quadratic terms. For problems without perturbation parameter, our results require weaker regularity assumptions on F and v than earlier ones, such as those of Hormander. For singularly perturbed functionals, we allow v to be larger than in previous works. To illustrate this, we apply our method to a nonlinear Schrodinger Cauchy problem with concentrated initial data studied by Texier-Zumbrun, and we show that our result improves significantly on theirs. | |
| dc.publisher.city | Paris | en |
| dc.identifier.citationpages | 25 | |
| dc.relation.ispartofseriestitle | Cahier de recherche CEREMADE, Université Paris-Dauphine | |
| dc.identifier.urlsite | https://hal.archives-ouvertes.fr/hal-01924328 | |
| dc.subject.ddclabel | Mathématiques | en |
| dc.description.ssrncandidate | non | |
| dc.description.halcandidate | non | |
| dc.description.readership | recherche | |
| dc.description.audience | International | |
| dc.date.updated | 2020-06-04T13:42:15Z | |
| hal.person.labIds | 60 | * |
| hal.person.labIds | 60 | * |
