简介:Inthispaper,wefirstshowtheglobalexistence,uniquenessandregularityofweaksolutionsforthehyperbolicmagnetohydrodynamics(MHD)equationsinR~3.ThenweestablishthatthesolutionswithinitialdatabelongingtoH~m(R~3)∩L~1(R~3)havethefollowingtimedecayrate:║▽~mu(x,t)║~2+║▽~mb(x,t)║~2+║▽~(m+1)u(x,t)║~2+║▽~(m+1)b(x,t)║~2≤c(1+t)~(-3/2-m)forlarget,wherem=0,1.
简介:Inthispaper,wegivetheholomorphicautomorphismgroupofthehigher-dimensionalgeneralizationofThullendomain.
简介:Inthepaper,weconsiderMoran-typesetsE_agivenbysequences{a_k}_(k=1)~∞and{n_k}_(k=1)~∞.weprovethatE_amaybedecomposeintothedisjointunionoflevelsets.Moreover,wedefinethreetypeofequivalencebetweentwodimensionfunctionsassociatedtotwoMorantypesets,respectively,andweclassifyMoran-typesetsbytheseequivalentrelations.
简介:Inthispaper,wemainlyinvestigateentiresolutionsofcomplexdifferentialequationswithcoefficientsinvolvingexponentialfunctions,andobtainthedynamicalpropertiesofthesolutions,theirderivativesandprimitives.Withsomeconditionsoncoefficients,forthesolutions,theirderivativesandtheirprimitives,weconsiderthecommonlimitingdirectionsofJuliasetandtheexistenceofBakerwanderingdomain.
简介:Inthispaper,firstweobtainsomenewfractionalintegralinequalities.Thenusingtheseinequalitiesandfixedpointtheorems,weprovetheexistenceofsolutionsfortwodifferentclassesoffunctionalfractionaldifferentialequations.
简介:Thispaperisconcernedwiththeharmonicequation(P_(■ε)):?u=0,u>0inB~nand?u/?ν+((n-2)/2)u=((n-2)/2)Ku~(n/(n-2)■ε)onS~(n-1)whereB~nistheunitballinR~n,n≥4withEuclideanmetricg_0,?B~n=S~(n-1)isitsboundary,KisafunctiononS~(n-1)andεisasmallpositiveparameter.Weconstructsolutionsofthesubcriticalequation(P_(-ε))whichblowupatonecriticalpointofK.WegivealsoasufficientconditiononthefunctionKtoensurethenonexistenceofsolutionsfor(P_(-ε))whichblowupatonepoint.Finally,weproveanonexistenceresultofsinglepeakedsolutionsforthesupercriticalequation(P_(+ε)).
简介:Inthispaper,weusecontractionmappingprinciple,operator-theoreticapproachandsomeuniformestimatestoestablishlocalsolvabilityoftheparabolic-hyperbolictypechemotaxissystemwithfixedboundaryin1-dimensionaldomain.Inaddition,localsolvabilityofthefreeboundaryproblemisconsideredbystraighteningthefreeboundary.
简介:WestudytheexistenceanduniquenessproblemforthenonhomogeneouspressurelessEulersystemwiththeinitialdensitybeingaRadonmeasure.Ouruniquenessresultisobtainedinthesamespaceastheexistencetheorem.Besides,bycounterexampleweprovethatHuang-Wang'senergyconditionisalsonecessaryforournonhomogeneoussystem.
简介:Inthispaper,usingpseudo-holomorphiccurvemethod,oneprovestheWeinsteinconjectureintheproductP_1×P_2oftwostronglygeometricallyboundedsymplecticmanifoldsundersomeconditionswithP_1.Inparticular,ifNisaclosedmanifoldoranoncompactmanifoldoffinitetopologicaltype,ourresultimpliesthattheWeinsteinconjectureinCP~2×T*Nholds.