简介：Themainpurposeofthispaperistwo-fold:(i)togeneralizeanexistenceresultforacompressiblegas-liquidmodelwithafrictiontermrecentlypublishedbyFriisandEvje[SIAMJ.Appl.Math.,71(2011),pp.2014–2047];(ii)toderiveauniquenessresultforthesamemodel.Amainingredientintheexistencepartistheobservationthatwecanconsiderweakerassumptionsontheinitialliquidandgasmass,andstillobtainanexistenceresult.Comparedtotheabovementionedwork,werelyonamorerefinedapplicationoftheestimatesprovidedbythebasicenergyestimate.Concerningtheuniquenessresult,weborrowideasfromFangandZhang[NonlinearAnal.TMA,58(2004),pp.719–731]andderiveastabilityresultunderappropriateconstraintsonparametersthatdeterminerateofdecaytowardzeroattheboundaryforgasandliquidmasses,andgrowthrateofmassesassociatedwiththefrictiontermandviscouscoefficient.

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简介：InthispaperweconsidertheBurger-Ginzburg-Landauequations,andprovetheexistenceoftheglobalattractorinwithfiniteHausdorffandfractaldimensions.

简介：LetB(resp.K,Bl,Kl)denotethesetofallnonemptybounded(resp.compact,boundedconvex,compactconvex)closedsubsetsoftheBanachspaceX,endowedwiththeHausdorffmetric,andletGbeanonemptyrelativelyweaklycompactclosedsubsetofX.LetB°standforthesetofallF∈Bsuchthattheproblem(F,G)iswell-posed.Weprovedthat,ifXisstrictlyconvexandKadec,thesetKl∩B°isadenseG_δ-subsetofKl\G.Furthermore,ifXisauniformlyconvexBanachspace,wewillprovemore,namelythatthesetB\B°(resp.K\B°,Bl\B°,Kl\B°)isa-porousinB(resp.K,Bl,Kl).Moreover,weprovethatformost(inthesenseoftheBairecategory)closedboundedsubsetsGofX,thesetK\B°isdenseanduncountableinK.

简介：Inthispaperwell-conditioningofboundaryvalueproblemsforsystemsofsecondorderdifferenceequa-tionsisstudied.First,asufficientconditionfortheexistenceofauniqueboundedsolution(forlargeenoughnumberofsteps)ofanassociatedhomogeneoussystemisgiven.Finally,asufficientconditionforwell-condi-tioning,intrinsicallyrelatedtotheproblemdataisproposed.

简介：TheauthorsconsiderthescatteringphenomenaofthedefocusingH~s-criticalNLS.ItisshownthatifasolutionofthedefocusingNLSremainsboundedinthecriticalhomogeneousSobolevnormonitsmaximalintervalofexistence,thenthesolutionisglobalandscatters.

简介：在线上的顺序三的方程被显示出全球性好的为概括Korteweg-deVries的起始的价值问题为不平的数据摆姿势。我们的证明基于Colliander，龙骨，Staffilani，Takaoka，和道介绍的多线性的估计和我方法。

简介：ThispaperisconcernedwiththeCauchyproblemofaseventhorderdispersiveequation.Weprovelocalwell-posednesswithinitialdatainSobolevspacesHs(R)fornegativeindicesofs>-11/4.

简介：Inthispaper,westudytheCauchyproblemforthe3DgeneralizedNavier-Stokes-Boussinesqequationswithfractionaldiffusion:{ut+（u·▽）u+v∧2αu=-▽p+θe（3）,e3=（0,0,1）T,θt+（u·▽）θ=0,Dicu=0.Withthehelpofthesmoothingeffectofthefractionaldiffusionoperatorandalogarithmicestimate,weprovetheglobalwell-posednessforthissystemwithα≥5/4.Moreover,theuniquenessandcontinuityofthesolutionwithweakerinitialdataisbasedonFourierlocalizationtechnique.Ourresultsextendonesonthe3DNavier-Stokesequationswithfractionaldiffusion.

简介：Inthispaper,weconsiderahydrodynamicflowofnematicliquidcrystalsystem.Weprovethelocalwell-posednessforthesysteminthecriticalLebesguespace,andstudythespace-timeregularityofthelocalsolution.

简介：SlowmotionforscalarAllen-Cahntypeequationisawell-knownphenomenon,precisemotionlawforthedynamicsoffrontshavingbeenestablishedfirstusingthesocalledgeometricapproachinspiredfromcentralmanifoldtheory(seetheresultsofCarrandPegoin1989).Inthispaper,theauthorspresentanalternateapproachtorecoverthemotionlaw,andextendittothecaseofmultiplewells.Thismethodisbasedonthelocalizedenergyidentity,andistherefore,atleastconceptually,simplertoimplement.Italsoallowstohandlecollisionsandroughinitialdata.

简介：关于我国标准算盘朝阳在我国流传很久的上二下五七珠大算盘的图式，始见于《魁本对相四言杂宇》明洪武年版。在明程大位《算法统宗》１５９２年系统介绍珠算以前，徐心鲁《金珠算法》二卷（１５７３）和柯尚迁《数学通轨》四卷（１５７８）都记有算盘图式。明来载育《算术...

简介：讨论了一种求不变因子的方法，利用不变因子与初等因子之间的关系，给出了一种求矩阵Jordan标准形的新方法．

简介：<正>《九年义务教育数学新课程标准》(以下简称新课程标准)体现了初中课程改革的最新成果,提出要重视培养学生的创新意识和实践探索的能力,应突出体现基础性,普及性和发展性,使数学教育面向全体学生,实现人人学有价值的数学,人人都能获得必需的数学,不同的人在数学上得到不同的发展。对教学内容和教学要求进行调整,以合理减轻学生的负担,是现行新课程标准的要求。

简介：<正>数学课堂教学过程是师生双方在数学教学目标指引下,以数学教材为中介,教师组织和引导学生主动掌握数学知识、发展数学能力、形成良好个性心理品质的认识与发展相统一的活动过程。

简介：本文建立了旋转抛物面聚焦枝的标准方程，导出了聚焦核的临界角，并讨论了焦平面与反射光锥的截线。

简介：在非标准分析框架下,用离散函数定义新广义函数,用差商定义其导数.对Schwartz广义函数以及更广的Gevrey超广义函数,文章证明了广义导数可以用差商表示.此外还给出了此新广义函数和Sobolev理论的关系.

简介：给出了同步求解矩阵若当标准型及过渡矩阵的一种新方法：行列互逆初等变换法．

简介：本文提出了求矩阵A的Jordan标准形的另一方法：利用rank(λ(E-A)^P的结果，得出了对应于特征(λi的Jordan块的阶数和个数，然后求出矩阵A的Jordan标准形．