Riemann Problem for First-Order Partial Equations Without the Convexity of a State Functions

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dc.contributor.authorRasulov, Mahir
dc.contributor.authorUlas, S. Ozgur
dc.date.accessioned2024-03-13T10:30:23Z
dc.date.available2024-03-13T10:30:23Z
dc.date.issued2015
dc.departmentİstanbul Beykent Üniversitesien_US
dc.description6th International Conference on Finite Difference Methods - Theory and Applications (FDM - T and A) -- JUN 18-23, 2014 -- Lozenetz, BULGARIAen_US
dc.description.abstractIn this work, the exact solution of the Riemann problem for first-order nonlinear partial equation with non-convex state function in Q(T) = {(x, t)vertical bar x is an element of I = (-infinity, infinity), t is an element of [0, T)} subset of R-2 is found. Here F is an element of C-2 (Q(T)) and F '' (u) change their signs, that is F(u) has convex and concave parts. In particular, the state function F (u) = -cos u on [pi/2, 3 pi/2] and [pi/2, 5 pi/2] is discussed. For this, when it is necessary, the auxiliary problem which is equivalent to the main problem is introduced. The solution of the proposed problem permits constructing the weak solution of the main problem that conserves the entropy condition. In some cases, depending on the nature of the investigated problem a convex or a concave hull is constructed. Thus, the exact solutions are found by using these functions.en_US
dc.description.sponsorshipUnit Rousse Angel Kancheven_US
dc.identifier.doi10.1007/978-3-319-20239-6_36
dc.identifier.endpage339en_US
dc.identifier.isbn978-3-319-20239-6
dc.identifier.isbn978-3-319-20238-9
dc.identifier.issn0302-9743
dc.identifier.scopus2-s2.0-84947087248en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage332en_US
dc.identifier.urihttps://doi.org/10.1007/978-3-319-20239-6_36
dc.identifier.urihttps://hdl.handle.net/20.500.12662/3317
dc.identifier.volume9045en_US
dc.identifier.wosWOS:000364326600036en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSpringer-Verlag Berlinen_US
dc.relation.ispartofFinite Difference Methods, Theory And Applicationsen_US
dc.relation.publicationcategoryKonferans Öğesi - Uluslararası - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectFirst order nonlinear partial differential equationsen_US
dc.subjectRiemann problemen_US
dc.subjectCharacteristicsen_US
dc.subjectWeak solutionen_US
dc.subjectShock waveen_US
dc.subjectConvex and concave hullen_US
dc.titleRiemann Problem for First-Order Partial Equations Without the Convexity of a State Functionsen_US
dc.typeConference Objecten_US

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