部分报告论文摘要Ginzburg-Landau方程的随机摄动摘要：该文讨论了一类具有白噪声干扰的Ginzburg-Landau方程的奇摄动问题。通过构造适当的格林函数，给出了该方程解的随机微分表达式，得到了其形式渐近展开式，并分析了该方程解的期望与方差，从而在方差的意义下，得到了解的余项估计。AHyperbolicLindstedt-PoincaréMethodforHomoclinicMotionofaKindofStronglyNonlinearAutonomousOscillatorsAbstract：AhyperbolicLindstedt-Poincarémethodispresentedfordeterminingthehomoclinicsolutionsofakindofnonlinearoscillators.Thecriticalvalueofthehomoclinicbifurcationparametercanbedeterminedinthisperturbationprocedure.ThegeneralizedLiénardoscillatorisstudiedindetail.Toillustratetheaccuracyofthepresentmethod,itspredictionsarecomparedwiththoseofRunge-Kuttamethod.Finiteelementanalysisforsingularlyperturbedadvection–diffusionRobinboundaryvalueproblems摘要：Weconsiderasingularlyperturbedadvection–diffusiontwo-pointRobinboundaryvalueproblemwhosesolutionhasasingleboundarylayer.Basedonpiecewiselinearpolynomialapproximation,finiteelementmethodisappliedontheproblem.Estimationoftheerrorbetweensolutionandthefiniteelementapproximationisgiveninenergynormonshishkin-typemesh.TheHighPerformanceComputingontheCrash-safetyAnalysisAbstract:Theinvestigationforthecomplexpropertiesinvarioustestingconditionfortheauto-crashsafetyanalysishavebeeninterestinganddifficultproblemsespeciallyinthestochasticmodellingprocess.Inthispaperanapplicationofanglevariationboundaryconditionarediscussedforthevirtualtestmethodsinthestructuredeformationsafetyanalysis.Themathematicalreviewandfiniteelementsimulationsaregiventoyieldfurtherstudyonthetheoreticalmodelandpracticaltestingstandardswiththestatisticalconclusion.右端函数间断的两阶半线性奇摄动边值问题摘要：本文讨论了一类阶半线性边值问题。。其中，右端函数关于有一个第一类间断点，从而退化解在该点也是间断的。文章的第一部分引入了两个纯边界层问题，把原问题看成是的光滑连接。在端点处的值为待定参数。第二部分通过假设的特征根不为负实数和，验证了边值问题的条件稳定性，并用边界层函数法构造了问题的渐近解。第三部分利用问题连接的光滑性，确定了参数，并证明了的存在性。第四部分把原问题放在边界条件框架下，证明了解得一致有效性并得到了余项估计。在文章的最后部分给出了两个的例子，在处分别一个分量间断和两个分量都间断，将数值解与它们的零次渐进解进行了比较。ANewSelf-adaptiveMethodforPoissonTypeSingularPerturbedProblems杜亮亮同济大学数学系Abstract:Aself-adaptivemeshlessnumericalmethodbasedonChebyshevTauMatrixMethod(CTMM)andDomainDecompositionMethod(DDM)ispresentedforPoisson-typesingularperturbedproblemswhichiscalledtheSelf-adaptiveChebyshevTauMatrixMethod(SCTMM).ChebyshevTauMatrixMethod(CTMM)isproposedbyW.K.andX.W.firstlytotreatthepoissonproblemsinirregulardomain.Anewself-adaptivemethodtodeterminethewidthofboundaryorinteriorlayerisgiveninthispaper.NumericalexperimentsareimplementedtoverifytheefficiencyofSCTMMindealingwithsingularperturbedproblems,andthenumericalresultsappearthatSCTMMisveryeffectiveandwithhighaccuracyforPoisson-typesingularperturbedproblems.MultiplicityResultsforp-LapacianBoundaryValueProblemsviaCriticalPointsTheorem杜增吉徐州师范大学数学科学学院摘要：通过创造性地构造可分的、自反的Banach空间和G-可导、序列弱下半连续的泛函，运用临界点定理研究P-Laplacian方程边值问题的特征区间的存在性以及多解性,实质推广和改进了参考文献中的主要结果。Acomputationalmethodforsolvingthird-ordersingularlyperturbedboundary-valueproblems耿发...
