简介：讨论变系数Euler-Bernoulli梁振动系统utt(x,t)+η(t)uxxxx(x,t)=0,0＜x＜1,0≤t≤T{u(0,t)=ux(0,t)=0,0≤t≤T-uxxx(1,t)+mutt(1,t)=-αut(1,t)+βuxxxt(1,t),0≤t≤T(1)uxt(1,t)=-γuxx(1,t),0≤t≤Tu(x,0)=u1(x),ut(x,0)=u2(x),0≤x≤1证明了该系统产生一个发展系统.

简介：考虑动态输出反馈控制下Euler-Bernoulli梁的振动抑制问题,证明了系统算子生成的C0-半群,不指数稳定但渐近稳定.且当初值充分光滑时,利用Riesz基方法估计出系统能量多项式衰减.

简介：讨论具有非线性耗散边界反馈的非均质Euler-Bernoulli梁的镇定问题.首先利用非线性半群理论和能量摄动方法,证明了文中所给出的非线性耗散边界反馈控制可以镇定闭环系统的能量,并导出了闭环系统的能量的衰减速度.

简介：提出几类Euler（欧拉）型微分方程。借助变量替换法、线性化法、降阶法、交换变量位置法及复合函数求导法则，转化为可求解的Euler方程。论证它们的可积性，扩大微分方程的可积范围。给出求解的方法及通积分的表达式．

简介：讨论弱耗散梁方程的能量衰退.通过构造辅助泛函的方法克服了一般的证明能量估计的方法在证明过程中所碰到困难,从而证明了如果记忆核是指数衰退的,那么能量也是指数衰退的.

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简介：利用Bernoulli多项式和Bernoulli函数，给出了连续可微函数的Bernoulli表示，并用这种表示来解决一类差分方程的通解问题。

简介：TheBernoulliconvolutionvλmeasureisshowntobeabsolutelycontinuouswithL2densityforalmostall1/2

简介：基于有限变形原理,采用微分几何的方法推导了不考虑剪切、转动惯量和翘曲影响的曲梁的三维变形的应力-应变关系.然后利用Hamilton变分原理推导了三维空间曲梁在考虑三个位移自由度和三个转动自由度下的非线性动力学方程.把得到的非线性动力学方程退化为面内圆弧拱的线性动力学方程,并与已有结果进行了对比.非线性动力学方程的建立为曲梁的非线性动力学分析做好了必要的准备.

简介：Basedonthetheoryofcalculusofvariation,somesuffcientconditionsaregivenforsomeEuler-LagrangcequationstobeequivalentlyrepresentedbyfiniteoreveninfinitemanyHamiltoniancanonicalequations.Meanwhile,somefurtherapplicationsforequationssuchastheKdVequation,MKdVequation,thegenerallinearEulerLagrangeequationandthecylindricshellequationsaregiven.

简介：TheregularsolutionsoftheisentropicEulerequationswithdegeneratelineardampingforaperfectgasarestudiedinthispaper.Andacriticaldegeneratelineardampingcoefficientisfound,suchthatifthedegeneratelineardampingcoefficientislargerthanitandthegasliesinacompactdomaininitially,thentheregularsolutionwillblowupinfinitetime;ifthedegeneratelineardampingcoefficientislessthanit,thenundersomehypothesesontheinitialdata,theregularsolutionexistsglobally.

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简介：Inthispaper,theuniquenessofstationarysolutionswithvacuumofEulerPoissonequationsisconsidered.Throughanonlineartransformationwhichisafunctionofdensityandentropy,thecorrespondingproblemcanbereducedtoasemilinearellipticequationwithanonlinearsourcetermconsistingofapowerfunction,forwhichtheclassicaltheory[4]'[9]oftheellipticequationsleadstheauthorstotheuniquenessresultundersomeassumptionsontheentropyfunctionS(x).Asanexample,theauthorsgettheuniquenessofstationarysolutionswithvacuumofEuler-PoissonequationsforS(x)=|x|θandθ∈{0}∪[2(N-2),+∞).

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简介：应用Jameson的有限体积法求解二维Euler方程，模拟叶栅跨音速流场，并运用当地时间步长和隐式残差平均技术加快收敛速度，计算结果与理论解和试验数据吻合良好，本文比较了采用两种不同的通量计算公式的计算结果。

简介：对于非线性四阶两点边值问题建立了一个孪生正解的存在定理.该边值问题通常描述了具有固定两端点的弹性梁的形变.

简介：通过选择适当的Banach空间并利用Leray-Schauder非线性抉择对于含各阶导数的非线性弹性梁方程u(4)(t)=f(t,u(t),u′(t),u″(t),u(t)),0t1,u(0)=u′(1)=u″(0)=u(''')(1)=0.建立了一个解的存在定理.在材料力学中,该方程描述了一端简单支撑,另一端被滑动夹子夹住的弹性梁的形变.这个存在定理说明只要非线性项满足某种线性增长条件该方程至少有一个解.

简介：TheconvergenceproblemofthefamilyofEuler-HalleymethodsisconsideredundertheLipschitzconditionwiththeL-average,andaunitedconvergencetheorywithitsapplicationsispresented.

简介：TheauthorsconsidertheEulerequationsforacompressiblefluidinonespacedimensionwhentheequationofstateofthefluiddoesnotfulfillstandardconvexityassumptionsandviscosityandcapillarityeffectsaretakenintoaccount.Atypicalexampleofnonconvexcon-stitutiveequationforfluidsisVanderWaals'equation.Thefirstordertermsofthesepartialdifferentialequationsformanonlinearsystemofmixed(hyperbolic-elliptic)type.Foraclassofnonconvexequationsofstate,anexistencetheoremoftravelingwavessolutionswitharbitrarylargeamplitudeisestablishedhere.Theauthorsdistinguishbetweenclassical(compressive)andnonclassical(undercompressive)travelingwaves.ThelatterdonotfulfillLaxshockinequali-ties,andarecharacterizedbytheso-calledkineticrelation,whosepropertiesareinvestigatedinthispaper.

简介：Thewell-posednessoftheinitialvalueproblemoftheEulerequationswasmainlydiscussedbasedonthestratificationtheory,andthenecessaryandsufficientconditionsofwell-posednessarepresentedforsomerepresentativeinitialorboundaryvalueproblem,thusthestructureofsolutionspaceforlocal(exact)solutionoftheEulerequationsisdetermined.Moreoverthecomputationformulasoftheanalyticalsolutionofthewell-posedproblemarealsogiven.