简介：这篇论文讨论加速为解决非线性的抛物线的方程的含蓄的计划的反复的方法。二个新非线性的反复的方法由theimplicit明确的伪说出--牛顿(IEQN)方法和衍生物免费的含蓄明确的伪--牛顿(DFIEQN)方法被介绍，在哪个结果从linearization的线性方程能保存原来的部分微分方程的抛物线的特征。重复方法的反复的顺序能集成二次的联盟者到含蓄的计划的答案，这被证明。而且与Jacobian免费Newton-Krylov(JFNK)方法相比，theDFIEQN方法有一些优点，例如，它的实现是容易的，并且它与一个明确的系数矩阵给一个线性代数学的系统，以便线性(内部)重复没被限制为Krylov方法。由IEQN，DFIEQN，JFNK和Picard重复方法的计算结果在理论的证实和这些方法的表演的比较被介绍。

简介：Abstract.OgrobjectinthisartlcleistodescribetbeGalerklnschemeandnonlin-eaxGalerkinschemefortheapproximationofnonlinearevolutionequations,andtostudythestabilityoftheseschemes.SpatialdiscretizatloncanbepedormedbyeitherGalerklnspectralmethodornonlinearGalerldnspectralmethod;timediscretizatlortisdonehyEulersin.heinewklchisexplicitorimplicitinthenonlinearterms.Accordingtothestabilityanalysisoftheaboveschemes,thestabilityofnonllneexGalerklnmethodisbetterthanthatofGalexklnmethod.

简介：各种各样的途径为解决许多连续全球优化问题被开发了。但是直到现在，更少的工作被奉献给由于固有的困难解决非线性的整数编程问题。这篇论文设法把一般非线性的整数编程问题转变成一个equivalent'专辑连续全球最小化问题。因此，任何有效全球优化算法能被用来解决非线性的整数编程问题。这结果将也在全球优化上支持研究。我们在场一个间隔Branch-and-Bound算法。数字实验证明这条途径是有效的。(作者摘要)11个裁判员。

简介：LetXdenoteacomplexanalyticmanifold,andletAut(X)denotethespaceofinvertiblemapsofagerm(X,a)toagerm(X,b);thisspaceisobviouslyagroupoid;roughlyspeaking,a'Liegroupoid'isasubgroupoidofAut(X)definedbyasystemofpartialdifferentialequations.ToafoliationwithsingularitiesonXoneattachessuchagroupoid,e.g.thesmallestonewhoseLiealgebracontainsthevectorfieldstangenttothefoliation.Itiscalled'theGaloisgroupoidofthefoliation'.Someexamplesareconsidered,forinstancefoliationsofcodimensionone,andfoliationsdefinedbylineardifferentialequations;inthislastcaseonerecuperatestheusualdifferentialGaloisgroup.

简介：Inthispaper,aBoussinesqhierarchyinthebilinearformisproposed.ABacklundtransformationforthishierarchyispresentedandthenonlinearsuperpositionformulaisprovedrigorously.

简介：Ageneralnonlinearconstitutivemodelisproposedformagnetostrictivematerials,basedontheimportantphysicalfactthatanonlinearpartoftheelasticstrainproducedbyapre-stressisrelatedtothemagneticdomainrotationormovementandisresponsibleforthechangeofthemaximummagnetostrictivestrainwiththepre-stress.Toavoidthecomplicityofdeterminingthetensorfunctiondescribingthenonlinearelasticstrainpart,thispaperproposesasimplifiedmodelbymeansoflinearizingthenonlinearfunction.Fortheconvenienceofengineeringapplications,theexpressionsofthe3-D(bulk),2-D(film)and1-D(rod)modelsare,respectively,givenforanisotropicmaterialandtheirapplicablerangesarealsodiscussed.BycomparisonwiththeexperimentaldataofaTerfenol-Drod,itisfoundthattheproposedmodelcanaccuratelypredictthemagnetostrictivestraincurvesinlow,moderateandhighmagneticfieldregionsforvariouscompressivepre-stresslevels.Thenumericalsimulationfurtherillustratesthat,foreithermagnetostrictiverodsorthinfilms,theproposedmodelcaneffectivelydescribetheeffectsofthepre-stressorresidualstressonthemagnetizationandmagnetostrictivestraincurves,whilenoneoftheknownmodelscancaptureallofthem.Therefore,theproposedmodelenjoyshigherprecisionandwiderapplicabilitythanthepreviousmodels,especiallyintheregionofthehighfield.

简介：为非强迫的优化在方法上介绍研究。学习的假设；主要结果；在简化Armijo类型下面的方法的集中性质衬里搜索。

简介：Thedynamicresponseofthenon-linearelasticsimplysupportedbeamsubjectedtoaxialforcesandtransverseperiodicloadisstudied.Melnikovmethodisusedtoconsiderthedynamicbehav-iorofthesystemwhosepost-bucklingpathissteady.Theeffectofthehigherordertermsinthecon-trollingequationistakenintoaccount.Itisfoundthatthefifth-ordertermshaveagreatinfluenceonthedynamicbehaviorofthesystem.Theresultshowsthatthereexisteitherhomoclinicorbitsorhete-roclinicorbitsinthesystem.Inthispaper,thecriticalvaluesofthesystementeringchaoticstatesaregiven.Thediagramofanexampleisshown.

简介：Theconjugategradientmethodforunconstrainedoptimizationproblemsvarieswithascalar.Inthisnote,ageneralconditionconcerningthescalarisgiven,whichensurestheglobalconvergenceofthemethodinthecaseofstrongWolfelinesearches.ItisalsodiscussedhowtousetheresulttoobtaintheconvergenceofthefamousFletcher-Reeves,andPolak-Ribiere-Polyakconjugategradientmethods.Thattheconditioncannotberelaxedinsomesenseismentioned.

简介：Someofthemathematicalpropertiesoftheinterfacebetweentwoincompressibleinviscidandimmisciblefluidswithdifferentdensitiesundertheinfluenceofaconstantgravityfieldgareinvestigated.ThepurposeofthispaperistoprovethatlinearlyunstablemodesforRayleigh-Taylorinstabilitiesgivebirthtononlinearinstabilitiesforthefullnonlinearsystem.Themainingredientisageneralinstabilitytheoreminananalyticframeworkwhichenablesustogofromlineartononlinearinstabilities.

简介：§1.IntroductionAssociatedwiththeeigenvalueproblem

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简介：Inthisletterthethree-dimensionalnonlinearHelmholtzequationisinvestigated,whichdescribeselectro-magneticwavepropagationinanonlinearKerr-typemediumsuchthatsixteenfamiliesofnewJacobiellipticfunctionsolutionsareobtained,byusingourextendedJacobianellipticfunctionexpansionmethod.Whenthemodulusm→1or0,thecorrespondingsolitarywavesincludingbrightsolitons,darksolitonsandnewlinesolitonsandsinglyperiodicsolutionscanbealsofound.

简介：Inthispaperwereviewoursomeresultsaboutthestronglysingular(discontinuous,measure,ordeltafunction)problemsfornonlinearhyperbolicequations.

简介：臼元素方法是新领域分解方法(DDM)舔withnonover子域。它能处理不同子域上的网孔不必越过接口，并且在邻近的子域上匹配discretizations排列的状况仅仅微弱地被强制。但是直到现在，为非线性的PDE有很小的工作。在这篇论文，我们将为与著名海军司烧方程有关的一个非线性的双性人泛音方程介绍一个臼类型莫利元素方法。最佳的精力和H~1标准估计在一个合理椭圆形的整齐假设下面被获得。

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简介：AclassofparallelnonlinearmultisplittingAORmethodsissetupbydirectlymultisplittingthenonlinearmappingF:DCR^n→R^nforsolvingthenonlinearsystemofequationsF(x)=0.Thedifferentchoicesoftherelaxationparameterscanyieldalltheknownandalotofnewrelaxationmethodsaswellasalotofnewrelaxationparallelnonlinearmultisplittingmethods.Thetwo-sidedapproximationpropertiesandtheinfluencesonconvergencefromtherelaxationparametersaboutthenewmethodsareshown,andthesufficientconditionsguaranteeingthemethodstoconvergegloballyarediscussed.Finally,alotofnumericalresultsshowthatthemethodsarefeasibleandefficient.

简介：Thesingularlyperturbednonlinearboundaryvalueproblemsareconsidered.Usingthestretchedvariableandthemethodofboundarylayercorrection,theformalasymptoticexpansionofsolutionisobtained.Andthentheuniformvalidityofsolutionisprovedbyusingthedifferentialinequalities.

简介：Thefollowingpartialdifferentialequationsarestudied:generalizedfifth-orderKdVequation,waterwaveequation,Kupershmidtequation,couplesKdVequation.Theanalyticalsolutionstotheseproblemsviausingvariousansaizesbyintroducingasecond-orderordinarydifferentialequationarefoundout.

简介：Theauthorsstudyhomogenizationofsomenonlinearpartialdifferentialequationsoftheform-div(a(hx,h^2x,Duh))=f,whereaisperiodicinthefirsttwoargumentsandmonotoneinthethird.Inparticularthecasewhereasatisfiesdegeneratedstructureconditionsisstudied.ItisprovedthatuhconvergesweaklyinW0^1,1(Ω)totheuniquesolutionofalimitproblemash→＋∞.Moreover,explicitexpressionsforthelimitproblemareobtained.