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Hyperbolic Boundary Value Problems for Symmetric Systems with Variable Multiplicities

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMETIVIER, Guy
hal.structure.identifierDepartment of Mathematics IU
dc.contributor.authorZUMBRUN, Kevin
dc.date.accessioned2024-04-04T03:18:38Z
dc.date.available2024-04-04T03:18:38Z
dc.date.issued2005
dc.identifier.issn0022-0396
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194429
dc.description.abstractEnWe extend the Kreiss–Ma jda theory of stability of hyperbolic initial– boundary-value and shock problems to a class of systems, notably in- cluding the equations of magnetohydrodynamics (MHD), for which Ma jda's block structure condition does not hold: namely, simulta- neously symmetrizable systems with characteristics of variable mul- tiplicity, satisfying at points of variable multiplicity either a “totally nonglancing” or a “nonglancing and linearly splitting” condition. At the same time, we give a simple characterization of the block struc- ture condition as “geometric regularity” of characteristics, defined as analyticity of associated eigenpro jections The totally nonglancing or nonglancing and linearly splitting conditions are generically satisfied in the simplest case of crossings of two characteristics, and likewise for our main physical examples of MHD or Maxwell equations for a crys- tal. Together with previous analyses of spectral stability carried out by Gardner–Kruskal and Blokhin–Trakhinin, this yields immediately a number of new results of nonlinear inviscid stability of shock waves in MHD in the cases of parallel or transverse magnetic field, and recovers the sole previous nonlinear result, obtained by Blokhin–Trakhinin by direct “dissipative integral” methods, of stability in the zero-magnetic field limit.
dc.language.isoen
dc.publisherElsevier
dc.title.enHyperbolic Boundary Value Problems for Symmetric Systems with Variable Multiplicities
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
bordeaux.journalJournal of Differential Equations
bordeaux.pagepp 61--134
bordeaux.volume211
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00113901
hal.version1
hal.popularnon
hal.audienceNon spécifiée
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00113901v1
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