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dc.contributor.authorNeves, Wladimir ( Orcid Icon 0000-0001-8538-8478 )
dc.contributor.authorSerre, Denis ( Orcid Icon 0000-0002-0725-4383 )
dc.date.accessioned2021-07-13T14:55:07Z
dc.date.available2021-07-13T14:55:07Z
dc.date.issued2005-11-07
dc.identifier.citationNeves, W., & Serre, D. (2005). Ill-posedness of the Cauchy problem for totally degenerate system of conservation laws. Electronic Journal of Differential Equations, 2005(124), pp. 1-25.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/13849
dc.description.abstractIn this paper we answer some open questions concerning totally degenerate systems of conservation laws. We study the augmented Born-Infeld system, which is the Born-Infeld model augmented by two additional conservations laws. This system is a nice example of totally degenerate system of conservation laws and, global smooth solutions are conjectured to exist when the initial-data is smooth. We show that this conjecture is false, for the more natural and general condition of initial-data. In fact, first we show that does not exist global smooth solution for any 2X2 totally degenerated system of conservation laws, which the characteristics speeds do not have singular points. Moreover, we sharpen the conjecture in Majda [20]. Under the same hypothesis of initial-data, we show that the Riemann Problem is not well-posed, which follows for weak solutions of the Cauchy Problem. In the end, we prove some results on the direction of well-posedness for the less physically initial-data.en_US
dc.formatText
dc.format.extent25 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectConservation lawsen_US
dc.subjectCauchy problemen_US
dc.subjectTotally degenerated systemsen_US
dc.subjectIll-poseden_US
dc.titleIll-posedness of the Cauchy problem for totally degenerate system of conservation lawsen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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