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1.
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
2.
For the system of differential equations(?)=r(t)v_1 (?)=-a(t)f(x)g(v)where a(t)>0,r(t)>0 for t≥t_0;f(x)>0 and is decreasing forx>0,g(y)>0,we give necessary and sufficient condition of a propersolution.a bounded proper solution or sotutions of two kinds of boundary value problems onan infinite interval [c,∞),c≥t_0.Several examples are given to illustrate the conditionsof these results. 相似文献
3.
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
4.
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
5.
王文洽 《应用数学和力学(英文版)》2004,25(2)
IntroductionWeconsiderthefollowingnonlinearBurgers’equation : u t u u x=ε 2 u x2 , 0 0 ,( 1 )withtheinitialandtheboundaryconditions u(x,0 ) =f(x) , 0 相似文献
6.
Introduction WeconsidertheperturbedcouplednonlinearSchr dingerequations(CNLS)iq1t=q1xx 2[|q1|2 |q2|2-ω2]q1 iε(^D1q1-r1),iq2t=q2xx 2[|q1|2 |q2|2-ω2]q2 iε(^D2q2-r2),(1)whereqjis2πperiodicandeveninx.rjisconstant,^Djisboundeddissipativeoperatorand assumedtotaketheform^Djqj=-αjqj βj^Bqj,(2)αjandβjarepositiveconstants,j=1,2.^BisaFouriertruncationofLaplaceoperator xx,i.e.,^Bcos(kx)=-k2cos(kx),k0isasmallperturbation parameter.Th… 相似文献
7.
Introduction FangShaomeiandGuoBoling[1]consideredthefollowingtimeperiodicproblemof dampedcouplednonlinearwaveequations:ut f(u)x-αuxx βuxxx 2vvx=G1(u,v) h1(x),vt-γvxx 2(uv)x g(v)x=G2(u,v) h2(x),(1)whereα,β,γareconstants,andγ>0,β≠0.Undertheperiodicboundaryconditions,the authorsobtainedtheuniqueexistenceofstrongsolutionsfortheabovesystem.InthispaperweshallconsiderbifurcationbehaviorofthetravellingwavesolutionsofEq.(1)inthecaseGi(u,v)≡0,hi(u,v)≡0(i=1,2).Letξ=x-ct,u=u(x-ct),where cis… 相似文献
8.
严子谦 《应用数学和力学(英文版)》1986,7(8):767-773
In this paper,the global existence of solutions to the IVP=Δu+g(t)f(u) (t>0),u|_(t=0)=u_0(x)and the (?)PVPu_t=Δu-g(t,x)f(u)(t>0,x∈Ω),u|_(t-0)=u|_(?)(?)is investigated. As has been done in [6]the (?)duction of factor g(t) or g(t.x) innonlinear term is to prevent(?) occurrance of blowing-up or quenching of solutions.It isshown in this paper that most of the restrictions on f,g and u_0 in the theorems of[6] maybe cancelled or relaxed,that the smallness of g is required only for t large,and thatunder certain conditions controlling initial state can avoid blowing-up. 相似文献
9.
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
10.
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
11.
In this paper, we consider an odd-order delay differential equation with positive and negative coefficients. New sufficient conditions that guarantee the oscillation of all solutions are presented. Our results extend and improve some known results. Next, these results are used for establishing oscillation criteria for hyperbolic delay differential equations with positive and negative coefficients corresponding to three sets of boundary conditions. 相似文献
12.
We consider a class of nonlinear partial difference equations with continuous variables. Some oscillation criteria are obtained
using an integral transformation and inequalities. 相似文献
13.
靳明忠 《应用数学和力学(英文版)》1994,15(9):867-875
OSCILLATIONTHEOREMSOFHIGHERORDERNONLINEARDELAYDIFFERENTIALEQUATIONSJinMing-zhong(靳明忠)(DepartmentofBasicCourses,YunnanInstitut... 相似文献
14.
王培光 《应用数学和力学(英文版)》2000,21(5):585-590
IntroductionDuetotheaccurenceofagreatdealofmathematicmodellingsdescribedinpartialfunctionaldifferentialequationsintheapplicationfieldsofmechanicsandcontroltheory[1],greatinterestwasarousedastothestudiesonthepropertyofthesolutionsofthistypeofequations.G… 相似文献
15.
欧阳华江 《应用数学和力学(英文版)》1992,13(6):587-596
To eliminate oscillation and overbounding of finite element solutions of classical heat conduction equation, the author and Xiao have put forward two new concepts of monotonies and have derived and proved several criteria. This idea is borrowed here to deal with generalized heat conduction equation and finite element criteria for eliminating oscillation and overbounding are also presented. Some new and useful conclusions are drawn. 相似文献
16.
In this paper, the sufficient condition for self-excited oscillation of dynamic systems with gap is given by using qualitative
method of differential equations. 相似文献
17.
李先义 《应用数学和力学(英文版)》2002,23(11):1331-1338
IntroductionConsiderthefollowingdelaydifferenceequationwithhigherorderxn+1=A0xp0n+ A1xp1 n- 1+… + Akxpkn-k (n=0 ,1 ,2 ,… ) ,( 1 )whereAi,pi ∈ [0 ,∞ ) (i=0 ,1 ,2 ,…k;k∈ 1 ,2 ,… ) ( 2 )andtheinitialconditionsx-k,x-k+1,… ,x- 1,x0 arearbitrarypositivenumbers.Somespecialcasesofk=1forEq .( 1 )havebeen… 相似文献
18.
This paper is dealing with the oscillatory properties of first-order neutral delay impulsive differential equations and the
corresponding inequalities with constant coefficients. The established sufficient conditions ensure the oscillation of every
solution of equations of this type. 相似文献
19.
李万同 《应用数学和力学(英文版)》2003,24(11):1273-1280
The asymptotic behavior of a class of nonlinear delay difference equation wax studied . Some sufficient conditions are obtained for permanence and global attractivity . The results can be applied to a claxs of nonlinear delay difference equations and to the delay discrete Logistic model and some known results are included. 相似文献
20.
CLCnumber:O175.2Documentcode:AolutionsofHyperbangPeiguangandGeWeigaolutionsofHyperbolicFunctionaWangPeiguangandGeWeigaolution... 相似文献