一类推广的无压Euler-Poisson方程组适定性理论

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7、，g¬¬▲½Euler-Poisson。ᐵ¯°：Euler-Poisson，Volpertí_，〉ឋ，ᭆ᳛1万方数据)*+,ᜧắË.ᦻABSTRACTWeconsideraclassofnonlinearhyperbolicsystems,whichgeneralizetheEuler-Poissonsystemfortheevolutionoffluidflowswithoutpressureterm.WestudytheinitialvalueproblemandestablishnewresultsevenfortheEuler-Poiss

8、onsystem.WegeneralizehereamethodintroducedbyLeFlochin1990(basedontheVolpertproductandtheLaxformula)andestablishawell-posedtheorywhenonecomponentofthesystemisameasure-valuedfunctionwhilethesecondonehasboundedvariation.Existenceisestablishedforgeneralinitialdata,whileuniquenessisguarant

9、eedonlywhentheinitialdatadoesnotgeneraterarefactioncenters.Wefirstsolveanonconservativeversionoftheproblemandconstructsolutionswithboundedvariation,.Thesolutionstothesystemsofinterestisthenobtainedbydifferentiation,whichprovidesuswithacompletetheoryofexistenceanduniquenessforbothformu

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