Ill-posedness of the Cauchy problem for totally degenerate system of conservation laws

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dc.contributor.authorNeves, Wladimir
dc.contributor.authorSerre, Denis
dc.date.accessioned2021-07-13T14:55:07Z
dc.date.available2021-07-13T14:55:07Z
dc.date.issued2005-11-07
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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent25 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationNeves, W., & Serre, D. (2005). Ill-posedness of the Cauchy problem for totally degenerate system of conservation laws. <i>Electronic Journal of Differential Equations, 2005</i>(124), pp. 1-25.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/13849
dc.language.isoen
dc.publisherTexas State University-San Marcos, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectConservation laws
dc.subjectCauchy problem
dc.subjectTotally degenerated systems
dc.subjectIll-posed
dc.titleIll-posedness of the Cauchy problem for totally degenerate system of conservation laws
dc.typeArticle

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