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hal.structure.identifierGran Sasso Science Institute [GSSI]
dc.contributor.authorMarchesani, Stefano*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorOlla, Stefano
HAL ID: 18345
ORCID: 0000-0003-0845-1861
*
dc.date.accessioned2019-02-19T10:27:59Z
dc.date.available2019-02-19T10:27:59Z
dc.date.issued2020
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18457
dc.language.isoenen
dc.subjecthyperbolic conservation laws
dc.subjectboundary conditions
dc.subjectweak solutions
dc.subjectvanishing viscosity,
dc.subjectcompensated compactness
dc.subject.ddc515en
dc.titleA note on the existence of L 2 valued solutions for a hyperbolic system with boundary conditions
dc.typeDocument de travail / Working paper
dc.description.abstractenWe prove existence of L2-weak solutions of a quasilinear wave equation with boundary conditions. This is done using a vanishing viscosity approximation with mixed Dirichlet-Neumann boundary conditions. In this settingwe obtain a uniform a priori estimate in L2, allowing us to use L2 Young measures, together with the classical tools of compensated compactness. We then prove that the viscous solutions converge to weak solutions of the quasili near wave equation strongly in Lp, for any p∈[1, 2), that satisfy, in a weak sense, the boundary conditions in the sense given by Definition 2.1.Furthermore, Clausius inequality is in force for these solutions.
dc.publisher.nameCahier de recherche CEREMADE, Université Paris-Dauphine
dc.publisher.cityParis
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphine
dc.relation.ispartofseriesnumber9
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01920905v1
dc.subject.ddclabelAnalyseen
dc.identifier.citationdate2020
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2020-05-12T11:49:41Z
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