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1.
LetXbeaBanachspace,S(X)andB(X)betheunitsphereandunitballofX ,respectively.ByX ,X denotethedualandtwicedualspaceofX ,respectively .Ifthereexistsafunctiong( · ,·) :S(X) ×S(X) →Rwhichsatisfiesanyε >0 ,x,y∈S(X)thereexistsδ(ε,x,y) >0 ,whenh <δ(ε,x,y)(‖x+hy‖ -‖x‖h -g(x ,y) <ε ,wesaythatXisGateauxdifferential (GD) ;ifinf‖y‖=1δ(ε ,x ,y) >0XisFrechetdifferential(FD) ;ifinf‖x‖ =1δ(ε,x,y) >0XisuniformGateauxdifferential (UGD)andif inf‖x‖ =‖y‖ =1δ(ε,x,y) >0Xisunif… 相似文献
2.
ntroductionLetΩ R2 beaboundeddomain .Weconsiderthefollowingnon_stationarynaturalconvectionproblem :Problem (Ⅰ ) Findu =(u1,u2 ) ,p ,andTsuchthat,foranyt1>0 ,ut- μΔu +(u· )u + p=λjT ((x ,y ,t) ∈Ω× (0 ,t1) ) ,divu =0 ((x ,y,t) ∈Ω× (0 ,t1) ) ,Tt-ΔT +λu· T =0 ((x,y,t) ∈Ω× (0 ,t1) ) ,u =0 ,T =0 ((x,y,t)∈ Ω× (0 ,t1) ) ,u(x ,y ,0 ) =0 , T(x,y,0 ) =f(x,y) ((x,y) ∈Ω) ,whereuisthefluidvelocityvectorfield ,pthepressurefield ,Tthet… 相似文献
3.
固定边矩形弹性薄板卡门大挠度与大振幅方程组的逼近解 总被引:2,自引:0,他引:2
1.大挠度问题图1所示的固定边矩形弹性薄板,其大挠度问题由下列卡门方程组定义:按文献考虑以下边界条件:当x=0及x=a 时:W=0(无挠度);((?)W)/((?)x)=0(无转角) (4)((?)~3φ)/((?)x~3) (2 μ)((?)~3φ)/((?)x(?)y~2)=0 (沿板边无法向位移) (5)((?)~2φ)/((?)x(?)y)=0 (没有阻止沿板边切向位移的力) (6)当y=0及y=b 时也有相同意义的边界条件如下: 相似文献
4.
带裂纹角钢形截面杆抗扭附度和第三型应力强度因子的计算 总被引:1,自引:0,他引:1
本文是作者前一工作的继续,文中讨论了开裂角钢形截面抗扭刚度和第三型应力强度因子的计算方法.对于图1所示截面,若令扭转问题中的应力函数为φ(x,y)=-x~2 u(x,y) (1)不难导出对于函数u(x,y)的定解问题为((?)~2u/(?)x~2) ((?)~2u/(?)y~2)=0,u|L=x~2 (2)其中L 表示截面的周边.同时抗扭刚度为D=μJ J=2(?)(-x~2 u(x,y))dxdy (3) 相似文献
5.
IntroductionIt’swell_knownthatthecomplicatedfundamentalsolution[1,2 ]forHelmholtzequationΔu(x) +k2 u(x) =0 (x∈Ω:boundedopenregioninR2 )isu (x,y) =-iH(2 )0 (k x-y ) 4,thusit’snotconvenientfornumericalcomputation .IfapplyingthesimplefundamentalsolutionofLaplaceequationu 0 (x ,y) =-ln|x-y|(2π) ,theexpressionforthesolutionofequationintheclosedregion Ωisc(y)u(y) + ∫Γu(x) u 0 (x,y) nx -u 0 (x ,y) u(x) n dsx =-k2∫Ωu(x)u 0 (x,y)dΩx.Astherightsideappearstheregionalintegrationinclu… 相似文献
6.
<正> 动量矩定理有多种形式,常用的形式可归纳如下:(1)对定矩心 o′的绝对动量矩定理(?)_0=L_0 (1)(2)在平动参考系 O′x′y′z′中对矩心 O′的相对 相似文献
7.
IntroductionInthispaper,westudiedakindofboundaryvalueproblems (BVPs)forsemi_linearretardeddifferentialequationwithnonlinearboundarycondition : εx″(t) =f(t,x(t) ,x(t-ε) ,ε) , t∈(0 ,1 ) ,(1 ) x(t) =φ(t,ε) , t∈[-ε0 ,0 ] ,h(x(1 ) ,x′(1 ) ,ε) =A(ε) ,(2 )whereε>0isasmallparameterandε0 isasufficientlysmallpositiveconstant.ThereweremanyresultsofstudyingonsingularlyperturbedboundaryvalueproblemforretardeddifferentialequationinRefs.[1~5] .Butthosestudiespossessedanesse… 相似文献
8.
多项式稳定性的一类新判据 总被引:5,自引:0,他引:5
给出了多项式没有一个根位于右半平面的必要条件(定理1),并由此引出“判定系数”,“子判定系数”等概念,获得多项式稳定性的“逐级判定法”。 又利用判定系数给出了几个实用的充分条件(定理2—定理5)。其中最有意义的是证明了 定理4 多项式f(x)=a_0 a_1x … a_nx~n(a_i>0)稳定的一个充分条件是 a_(i-1)a(i 2)≤0.4655a_ia(i 1) (i=1,2,…,n-2) 多项式稳定性的这类判据为判定或设计稳定的线性系统提供了方便。 相似文献
9.
For the system of differential equations x=r(t)y,y=-a(t)f(x)g(y) where a(t)>0, r(t)>0 for t≥t; f(x) >0 and is decreasing for x>0 g(y)>0, we give necessary and sufficient condition of the existence of a proper solution, a bounded proper solution or solutions of two kinds of boundary value problems on an infinite interval [c,∞] c≥tg. Several examples are given to illustrate the conditions of these results. 相似文献
10.
本文遵循Bogoliubov积分流形的思想,研究系统φ=w(x) φ(t, x, φ),=εX(t, x, φ)在x空间某点或某高维超曲面之ε领域内存在稳定积分流形之充分条件。当x空间某点为系统之孤立共振点或某高维超曲面为系统之孤立共振超曲面时,所得定理可证明文献[4]中有关多频共振稳定性判别准则之正确性。 相似文献
11.
本文是作者前二论文的推广,在解决厚壁T和槽形截面悬梁弯曲问题时,首先通过简单代换,把应力函数φ(x,y)的边值问题化为Laplace方程的Dirichlet问题,然后把所考虑区域分割成几个矩形,并在分割线上设立待定函数,利用调和函数的延拓定理,即Duhem定理,便可解决待解的边值问题和得出弯曲中心的算式,容易看出,在所讨论问题中,调和函数延拓定理和沿着分割线的剪应力连续性等价。 相似文献
12.
本文用全纯函数表示微分方程△f(x,y)-λ(~2)f(x,y)=0的一般解,粮据全纯函数的Bekya积分表示法,建立了复数域内的边界积分方程并针对各种边界条件下Reissner型夹层板、Hoff型夹层板进行了数值求解。 相似文献
13.
本文用全纯函数表示微分方程△f(x,y)-λ(~2)f(x,y)=0的一般解,粮据全纯函数的Bekya积分表示法,建立了复数域内的边界积分方程并针对各种边界条件下Reissner型夹层板、Hoff型夹层板进行了数值求解。 相似文献
14.
曾六川 《应用数学和力学(英文版)》2003,24(12):1421-1430
IntroductionThroughoutthispaperweassumethatEisarealBanachspace ,E isthedualspaceofE ,DisanonemptysubsetofEandJ:E →2 E isthenormalizeddualitymappingdefinedbyJ(x) =f∈E :〈x ,f〉=‖x‖·‖f‖,‖f‖=‖x‖, x∈E . Definition 1 LetT :D →Dbeamapping .1 )Tissaidtobeasymptoticallynonexpansive[1],ifthereexistsasequence kn [1 ,∞)withlimn→∞kn =1suchthat ‖Tnx-Tny‖≤kn‖x-y‖forall x ,y∈D ,n≥0 ;(1 ) 2 )Tissaidtobeofasymptoticallynonexpansivetype[2 ],if lims… 相似文献
15.
Singular perturbation of nonlinear vector boundary value problem 总被引:2,自引:1,他引:1
In this paper we study the perturbed boundary value problem of the form dx/dt=f(x,y,t;ε), εdy/dt=g(x,y,t;ε), a_1(ε)x(0,ε)+a_2(ε)y(0,ε)=a(ε) b_1(ε)x(1,ε)+εb_2(ε)y(1,ε)=β(ε)in whichx,f,β∈E~m, y,g,a∈E~n, 0<ε(?)1and a_1(ε), a_2(ε), b_2(ε)and b_2(ε) are matrices of the appropriate size. Under the condition that g_y(t) is nonsingular and other suitable restrictions, the existence of the solution is proved, the asymptotic expansion of solution of order n is constructed, and the remainder term is estimated. 相似文献
16.
江福汝 《应用数学和力学(英文版)》1991,12(2):121-129
In this paper,we consider the boundary value problems of the formsy″-f(x,ε)y′ g(x,ε)=0 (-a≤x≤b,0≤ε《1 )y(-a)=a,y(b)=βwhere f(x,0)has several and multiple zeros on the interval[-a,b].The conditions forexhibiting boundary and interior layers are given,and the corresponding asymptoticexpansions of solutions are constructed. 相似文献
17.
张汉林 《应用数学和力学(英文版)》1997,18(5):503-510
I.IntroductionWeconsiderinthispaperboundaryvalueproblemofquasilineardifferentialequationby# pi(x,y)y' g(x,y)=0,a相似文献
18.
1 IntroductionandProblemWeshallstudytheoptimalcontrolproblemsgovernedbynonlinearparabolicvariationalinequalitiesoftheformy′+Ay +β(y) ∈Bu+f(a.e .(x,t)∈Q =Ω× [0 ,t]) ,y(0 ) =y0 , ( )withthestateconstraintF(y) S ,andthecostfunctionalI(y,u) .Whereβisadiscontinuous,nonlinearandnonmonotonemulti_valuedmapping .Theoptimalcontrolproblemsofthedifferentialsystemshavebeenstudiedforalongtime.Manyscholars,suchasJ.L .Lions ,V .Barbu ,D .Tiba,andF .Mignotetal.,haveresearchedtheoptimalcontrolpr… 相似文献
19.
<正> Liouville 和 Green 在1837年同时考虑了如下的二阶线性常微分方程d~2y/dx~2+[λ~2q_1(x)+q_2(x)]y=0 (1)其中 q_1(x)在区间[a,b]中有二阶连续导数,且q_1(x)>0 (当 x∈[a,b]) (2)q_2(x)在[a,b]中连续,且 相似文献
20.
In this paper,we study the singular perturbation of boundary value problem of systemsfor quasilinear ordinary differential equations:x′=f(t,x,y,ε),εy″=g(t,x,y,ε)y′ h(t,x,y,ε),x(0,ε)=A(ε),y(0,ε)=Bε,y(1,ε)=C(ε)where xf.y,h,A,B and C belong to R″and a is a diagonal matrix.Under the appropriateassumptions,using the technique of diagonalization and the theory of differentialinequalities we obtain the existence of solution and its componentwise uniformly validasymptotic estimation. 相似文献