简介：这份报纸是一个continue工作[4,5]。在以前的二份报纸，我们与看情况时间的抑制术语学习了多维的可压缩的Euler方程的Cauchy问题--(1+t)u，在此0并且>0是常数。我们显示出那，为所有0并且>0，Cauchy问题的光滑的答案全球性存在或在有限时间骤起。在现在的纸，而不是Cauchy问题，我们在一半考虑起始边界的价值问题空间有空间尺寸d=的d+2,3。在方程和液体涡度的特殊结构的帮助下，我们克服困难从边界效果产生。我们证明那在那里存在0的一个全球光滑的解决方案<1当起始的数据接近它的平衡状态时。另外，液体涡度的指数的腐烂将也被建立。

简介：Inthispaper,thefixedpointtheoremisappliedtoinvestigatetheexistenceofsolutionsofSturm-LiouvilleboundaryvalueproblemsfornonlinearsecondorderimpulsivedifferentialequationsinBanaehspaces.

简介：ＥＸＩＳＴＥＮＣＥＯＦＷＥＡＫＳＯＬＵＴＩＯＮＳＯＦ２－ＤＥＵＬＥＲＥＱＵＡＴＩＯＮＳＷＩＴＨＩＮＩＴＩＡＬＶＯＲＴＩＣＩＴＹω＿０∈Ｅ（ｌｏｇ￣＋Ｌ）￣α（α＞０）ＪＩＵＱＵＡＮＳＥＮ（ＩｎｓｔｉｔｕｔｅＯｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ｔ...

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简介：Thispaperdealswiththemixedinitial-boundaryvalueproblemofDirichlettypeforthenonlinearelastodynamicsystemoutsideastar-shapeddomain.Thealmostglobalexistenceofsolutionwithsmallinitialdatatothisproblemisprovedandalowerboundforthelifespanofsolutionsisgiven.

简介：Westudyboundaryvalueproblemsforfractionalintegro-differentialequationsinvolvingCaputoderivativeoforderα∈(n-1,n)inBanachspaces.ExistenceanduniquenessresultsofsolutionsareestablishedbyvirtueoftheHolder'sinequality,asuitablesingularGronwall'sinequalityandfixedpointtheoremviaaprioriestimatemethod.Atlast,examplesaregiventoillustratetheresults.

简介：Inthispaper,weinvestigatetheglobalexistenceandlongtimebehaviorofstrongsolutionsforcompressiblenematicliquidcrystalflowsinthreedimensionalwholespace.TheglobalexistenceofstrongsolutionsisobtainedbythestandardenergymethodundertheconditionthattheinitialdataareclosetotheconstantequilibriumstateinH~2-framework.IftheinitialdatasinL~1-normarefiniteadditionally,theoptimaltimedecayratesofstrongsolutionsareestablished.WiththehelpofFouriersplittingmethod,onealsoestablishesoptimaltimedecayratesforthehigherorderspatialderivativesofdirector.