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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorEkeland, Ivar
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorSéré, Eric
HAL ID: 171149
dc.date.accessioned2019-02-25T15:12:28Z
dc.date.available2019-02-25T15:12:28Z
dc.date.issued2019
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18489
dc.language.isoenen
dc.subjectlinear functional equationsen
dc.subjectnonlinear Schrödinger Cauchy problemen
dc.subject.ddc515en
dc.titleA surjection theorem for singular perturbations with loss of derivativesen
dc.typeDocument de travail / Working paper
dc.description.abstractenIn this paper we introduce a new algorithm for solving nonlinear functional equations which admit a right-invertible linearization, but such that the inverse loses derivatives. 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. We apply our method to a singular perturbation problem with loss of derivatives studied by Texier-Zumbrun. We will compare the two results and we will show that ours improves significantly on theirs, when applied, in particular, to a nonlinear Schrödinger Cauchy problem with highly oscillatory initial data.en
dc.identifier.citationpages24en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01924328en
dc.subject.ddclabelAnalyseen
dc.identifier.citationdate2019-01
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2019-02-25T15:09:09Z
hal.author.functionaut
hal.author.functionaut


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