共查询到20条相似文献,搜索用时 15 毫秒
1.
1.引言为了用有限维常微分方程来研究Navier七lobes(N七)方程的长时间动力学行为,Foias,Sell和Temaml]引入了耗散系统惯性流形的概念.但惯性流形存在的一个相当苛刻的条件一谱间隔条件一是包括N习方程在内的很多耗散系统无法满足的.因此,Foias,Manlea和TemamZ]随后又提出了近似惯性流形的概念.近似惯性流形也是一个光滑的Lipschitz流形,所有原方程的解在时间充分大时,将被吸引进入该流形的一个三邻域中.因其存在性不需要谱间隔条件来保证,从而可证明包括N-S方程在内的一大类耗散系统存在近似惯性流形.利用近似惯性… 相似文献
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APPROXIMATEINERTIALMANIFOLDSTOTHENAVIER-STOKESEQUATIONS王碧祥兰州大学,邮编:730000APPROXIMATEINERTIALMANIFOLDSTOTHENAVIER-STOKESEQUATIO... 相似文献
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本文研究一类二阶常微分方程解的渐近性态,假设方程具有正阻尼及适当保证所有解有界的条件成立,我们证明了每个解收敛于奇点,该结果能够用于系统的奇点集是不可数的情形。 相似文献
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0IntroductionInertialmanifolds(IM)arenewobjectsthathavebeenintroducedinrelationwiththestudyoflargetimebehaviorofnonlineardissipativePDE,see[1].In[2],theyareextendedtodiscretizeddynamicsstemmingfromdissipativePDE.Frommathematicalpointofview,thesearesmootllfiniteLipschitzmanifoldsthatareinviantbytheflowofassociatedsolutions,andattractallthetrajectorieswithexponentialspeed,see[1].Fromphysicalpointofview,IMmodeltheinteractionlawsbetweensmallandlargestructureofaturbulentflow,andrepresentsitspe… 相似文献
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The present paper deals with the long-time behavior of a class of nonautonomous retarded semilinear parabolic differential equations. When the time delays are small enough and the spectral gap conditions hold, the inertial manifolds of the nonautonomous retard parabolic equations are constructed by using the Lyapunov-Perron method. 相似文献
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一类二阶延迟微分方程梯形方法的延迟依赖稳定性分析 总被引:1,自引:0,他引:1
本文涉及一类二阶延迟微分方程数值方法的稳定性研究.通过运用边界轨迹法,分析了梯形方法的延迟依赖稳定区域并找到其准确边界.随后建立了解析和数值稳定区域的联系并从理论上证明了梯形方法能完全保持模型问题的延迟依赖稳定性. 相似文献
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In this paper, we present some new asymptotic results for a second order elliptic differential equations by using integral averaging and completing square technique. 相似文献
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By the averaging method of frst order, we study in this work the limit cycles for a class of second order diferential equations and Dufng diferential equations which can be seen as a particular perturbation of the harmonic oscillator. 相似文献
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董莹 《Annals of Differential Equations》1997,(3)
W(3considerthesecondor0andf(y)eC(--co,co)isTI(,11-d(3(\1'(3asillginy,andsat,is;ftes7/[(:!/)>0,if7//0(2)Assumef(y)satisfiessublinea,rconditionThroughoutthepaperswerestrictourattentiolloillytot-… 相似文献
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GEVREY CLASS REGULARITY AND APPROXIMATE INERTIAL MANIFOLDS FOR THE NEWTON-BOUSSINESQ EQUATIONS 总被引:2,自引:0,他引:2
§1.IntroductionApproximateinertialmanifoldsarerelatedtothestudyoflongtimebehaviourofsolutionsofdisipativepartialdiferentialeq... 相似文献
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关于一类二阶非线性双曲型方程全离散有限元方法的稳定性和收敛性估计 总被引:1,自引:0,他引:1
刘小华 《高等学校计算数学学报》2002,24(1):15-22
1 引 言考虑如下混合问题 :φ( x,u) utt- di,j=1 xi( aij( x,u) u xj) - di=1bi( x,u) uxi =f( x,u) ( x,t)∈Ω× [0 ,T]u( x,0 ) =0 , ut( x,0 ) =0 x∈Ωu( x,t) =0 ( x,t)∈ Ω× [0 ,T]( 1 .1 )这里 utt= 2 u t2 ,uxi= u xi;Ω是 Rd 中充分光滑的有界开域 ,边界 Ω光滑 .对于 φ( x,u)中仅含有 x,或 φ( x,u)≡ 1的线性或非线性双曲型方程的半离散或全离散有限元方法的研究已有 [1 ] -[4 ] .这些文献定义了线性[1 ] [4] 或非线性[2 ] 或预测—校正[4] 全离散有限元格式 ,然后将原方… 相似文献
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1FormulationofirregularObliqueDerivativeProblemLetDbean(N 1)-connecteddomainwithboundaryr=UU=,r,6Cj(0相似文献
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一类二阶非线性阻尼微分方程的振动性 总被引:34,自引:0,他引:34
研究了一类二阶非线性阻尼微分方程解的振动性,建立了三个新的振动性定理,推广了Cecchi M和Marini M(Rocky Mount J Math,1992,22:1259-1276)的结果. 相似文献
15.
二阶多时滞非线性微分方程的周期解 总被引:2,自引:0,他引:2
张保生 《纯粹数学与应用数学》1998,14(4):62-66
研究二阶系数非线性多时滞微分方程ω周期解的存在性,得到了ω周期解存在的充分条件。 相似文献
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一类三阶拟线性发展方程的整体解 总被引:1,自引:0,他引:1
杨志坚 《高校应用数学学报(A辑)》1998,13(1):31-38
本文研究一类三阶拟线性发展方程utt-Δut+ut=ni=1xiσi(uxi),(x,t)∈Ω×(0,T)的初边值问题,其中ΩRn(n≥1)为一有界域.证明了只要σi(s)∈C1,σ′i(s)(i=1,…,n)有界并且初始函数满足一定的条件,则上述问题存在唯一的整体弱解. 相似文献
17.
ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF SECOND ORDER NONLINEAR ELLIPTIC DIFFERENTIAL EQUATIONS 总被引:1,自引:0,他引:1
徐志庭 《数学物理学报(B辑英文版)》2001,21(1)
1 IntroductionTlle problem of obtaining sufficient conditions to ensure that al1 solutions of second orderordinary differential equations with an "integrally smal" coefficiellt are oscillatory'has beenstudied by many authors [cft1-4]] and other referellces cited therein. Recently, the paPers[cf[5],[6]] have discussed the asymptotiC properties of the solutions Of the follOwing equatious(a(f)W(x)X,), q(t)i(x) = c(t),(g(f, T)X,), q(t)f(x) = e(t),here q(f) is allowed to challge sign. In thi… 相似文献
18.
Jinjun Fan Fangfang Han 《Annals of Differential Equations》2014,(3):282-290
In this paper, we consider the existence of positive solutions to a three-point boundary value problem for second order dynamic equations with derivative on time scales.Applying Leggett-Williams fixed point theorem, we obtain at least three positive solutions to the problem. An example is also presented to illustrate the applications of the results obtained. 相似文献
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OSCILLATION THEOREMS FOR A CLASS OF SECOND ORDER NEUTRAL DIFFERENTIAL EQUATIONS OF EMDEN-FOWLER TYPE
Some oscillation theorems are established by the averaging technique for a class of second order neutral differential equations of Emden-Fowler type. Our results essentially improve some known results in the previous literature. 相似文献