简介：Inthispaperweconsiderthefollowingproblemui=△u^m+bi(u^n)xLetu=u(x,t)beacontinuousweaksolutionoftheequationinR^N×(0,T)forsomeT>0.Thenweconclude;CorrespondingtouthereisauniquenonnegativeBorelmeasurevonR^Nwhichistheinitialtraceofu;thereistheglobalinequalityofHarnacktypeforu;theinitialtracevmustbelongtoacertaingrowthclass;consequently,bycombiningtheresultsmentionedaboveau-niquenessconclusionisestablished.
简介：Inthispaperweosiderthefollowingprolemut=△u^m+bi(u^n)xiwherethesummationconventionisused.Wecalltheequationasporousmediumequationwithconvection.Letu=u(x,t)beacontinuousweaksolutionoftheequationinR^N×(0,T)]forsomeT>0,ThenwecanestablishBPCestimatesandtheintrinsicHarnackinequalityforthesolutionoftheequationjustasthestandardequationdiscussedbyotherauthorspreviously.Thisworklayamainfoundationofstudyingotherpropertiesofthisproblemfurther.
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