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Viscous boundary layers in hyperbolic-parabolic systems with Neumann boundary conditions

hal.structure.identifierLaboratoire d'Analyse, Topologie, Probabilités [LATP]
dc.contributor.authorGUÈS, Olivier
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMETIVIER, Guy
hal.structure.identifierDepartment of Mathematics [Chapel Hill]
dc.contributor.authorWILLIAMS, Mark
hal.structure.identifierDepartment of Mathematics IU
dc.contributor.authorZUMBRUN, Kevin
dc.date.accessioned2024-04-04T02:22:47Z
dc.date.available2024-04-04T02:22:47Z
dc.date.created2012
dc.date.issued2014
dc.identifier.issn0012-9593
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189676
dc.description.abstractEnWe initiate the study of noncharacteristic boundary layers in hyperbolic-parabolic problems with Neumann boundary conditions. More generally, we study boundary layers with mixed Dirichlet--Neumann boundary conditions where the number of Dirichlet conditions is fewer than the number of hyperbolic characteristic modes entering the domain, that is, the number of boundary conditions needed to specify an outer hyperbolic solution. We have shown previously that this situation prevents the usual WKB approximation involving an outer solution with pure Dirichlet conditions. It also rules out the usual maximal estimates for the linearization of the hyperbolic-parabolic problem about the boundary layer. Here we show that for linear, constant-coefficient, hyperbolic-parabolic problems one obtains a reduced hyperbolic problem satisfying Neumann or mixed Dirichlet--Neumann rather than Dirichlet boundary conditions. When this hyperbolic problem can be solved, a unique formal boundary-layer expansion can be constructed. In the extreme case of pure Neumann conditions and totally incoming characteristics, we carry out a full analysis of the quasilinear case, obtaining a boundary-layer approximation to all orders with a rigorous error analysis. As a corollary we characterize the small viscosity limit for this problem. The analysis shows that although the associated linearized hyperbolic and hyperbolic--parabolic problems do not satisfy the usual maximal estimates for Dirichlet conditions, they do satisfy analogous versions with losses.
dc.language.isoen
dc.publisherSociété mathématique de France
dc.title.enViscous boundary layers in hyperbolic-parabolic systems with Neumann boundary conditions
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
bordeaux.journalAnnales Scientifiques de l'École Normale Supérieure
bordeaux.pagepp 177-239
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue47
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00779851
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00779851v1
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