Show simple item record

dc.contributor.authorGlass, Olivier
dc.contributor.authorLeFloch, Philippe F.
dc.date.accessioned2011-10-10T14:27:58Z
dc.date.available2011-10-10T14:27:58Z
dc.date.issued2007
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/7147
dc.language.isoenen
dc.subjectCauchy problemen
dc.subjectPDEsen
dc.subject.ddc515en
dc.titleNonlinear Hyperbolic Systems: Nondegenerate Flux, Inner Speed Variation, and Graph Solutionsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study the Cauchy problem for general nonlinear strictly hyperbolic systems of partial differential equations in one space variable. First, we re-visit the construction of the solution to the Riemann problem and introduce the notion of a nondegenerate (ND) system. This is the optimal condition guaranteeing, as we show it, that the Riemann problem can be solved with finitely many waves only; we establish that the ND condition is generic in the sense of Baire (for the Whitney topology), so that any system can be approached by a ND system. Second, we introduce the concept of inner speed variation and we derive new interaction estimates on wave speeds. Third, we design a wave front tracking scheme and establish its strong convergence to the entropy solution of the Cauchy problem; this provides a new existence proof as well as an approximation algorithm. As an application, we investigate the time regularity of the graph solutions (X,U) introduced by LeFloch, and propose a geometric version of our scheme; in turn, the spatial component X of a graph solution can be chosen to be continuous in both time and space, while its component U is continuous in space and has bounded variation in time.en
dc.relation.isversionofjnlnameArchive for Rational Mechanics and Analysis
dc.relation.isversionofjnlvol185en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2007
dc.relation.isversionofjnlpages409-480en
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00205-006-0046-0en
dc.identifier.urlsitehttp://arxiv.org/abs/math/0701041v1en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelAnalyseen


Files in this item

FilesSizeFormatView

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record