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1.
1 IntroductionIn this paper,we firstprovide a generalized difference method for the two-dimension-al Navier-Stokes equations by combining the ideas of staggered scheme[6] and generalizedupwind scheme [4 ] in space,and by backward Euler time-stepping.Then we apply theabstractframework of[7] to prove its long-time convergence.The outline of this paper is as follows:In§ 2 we state the generalized differencemethod.In§ 3 we provide some lemmas.In§ 4 we study the one-sided Lipschitz condi-tio… 相似文献
2.
§ 0 .Introduction We consider the numerical approximations of the dynamical systems governed bysemilinear parabolic equations,which are discretized by Galerkin and nonlinear Galerkinmethods in space,and by Runge-Kutta method in time.The numerical approximationson a finite time interval have already been widely studied(see[1 ]— [5] ) .We areconcerned with the long-time convergence and error estimates.This article is composedof three parts. In part ,we provide an abstract framework. In§… 相似文献
3.
The bilinear from a(·,·)on the real Hilbert space is said to be coercive if there is a α>0) such that α(v,v)≥α‖v‖_H v∈H. (0.1)Assume that α(·,·)is a bilinear continuous and coercive form on H.Then, giving a f∈H′arbitrarily,There exists a unique u∈H such that α(u,v) = f(v). (0.2)Furthermore, u depends continuously on f. This is the Lax-Milgrarm Theorem obtained in 1954.In 1972, A. K. Aziz[1] improved the condition (0.1) and obtained the sufficient condition of Eq. (0.2) being Well-posed.In this paper,by different method,we proved, more simply, this sufficient condition in §1. Furthermore, we proved that this sufficient condition is also the necessary one. In §2 we improved the error estimate of approximate solution of (0.2). which was obtained by Céa[3] in 1964. In §3 we discussed the Well-posed problem of Eq.(2), when a(·, ·) is monotonic. This result may be considered as a generalization of the dffinition of coercive,and the Lax-Milgram Theorem as a special example. In §4 we exte 相似文献
4.
邬弘毅 《高校应用数学学报(英文版)》2002,17(2)
§ 1 IntroductionB-spline curve plays an important role in CAGD.Cn-continuous B-spline curve of de-gree n+ 1 has local support of length n+ 2 [1 ] .In order to modify the shape of a curve insmaller range,the length of its supportshould be as shortas possible.The interpolation ofa set of given data points with the B-spline curve generally needs to solve a system of lin-ear equations or to insert some additional control points[2— 5] .Besides,the global approxi-mation of the control polygon … 相似文献
5.
We consider the n-dimensional modified quasi-geostrophic(SQG) equations δ_tθ + u·▽θ+kΛαθ=0, u = Λα-1R⊥θ with κ 0, α∈(0, 1] and θ0∈ W1,∞(Rn). In this paper, we establish a different proof for the global regularity of this system. The original proof was given by Constantin, Iyer, and Wu[5], who employed the approach of Besov space techniques to study the global existence and regularity of strong solutions to modified critical SQG equations for two dimensional case.The proof provided in this paper is based on the nonlinear maximum principle as well as the approach in Constantin and Vicol [2]. 相似文献
6.
§1. Introduction In the paper [1], Pacella and Tricarico proved that the existence of infinitely many critical points of even functional integral from Ω to (F(x,u,Du)dx) in space W_0~(1,2). As far as our knowledge goes, the paper [1] is the first investigation of general functional integral from Ω to (F(x,u,Du)dx) in Hilbert space W_0~(1,2), but the techniques used in the paper[1], was restricted to Hilbert space. In the same year as when [1] had published, we independently proved [2] the 相似文献
7.
是嘉鸿 《数学物理学报(B辑英文版)》1984,(3)
§ 1 Introduction The investigating of the existence of globally smooth solutions or the formation of singularities of the solutions for semilinear parabolic equations is of much importance in the theory of partial differential equation as well as in the application. The blowing up of the solutions is an interesting phenomenon and has been pointed out by many authors in various cases, such as by S. Kaplan [1], C. V. pao[2], H. Kawarada[3]etc. In[4], Chen studied the problem of 相似文献
8.
Ju-liangZhang Xiang-sunZhang Yong-meiSu 《应用数学学报(英文版)》2004,20(4):557-572
In this paper, we analyze the global and local convergence properties of two predictor-corrector smoothing methods, which are based on the framework of the method in [1], for monotone linear complementarity problems (LCPs). The difference between the algorithm in [1] and our algorithms is that the neighborhood of smoothing central path in our paper is different to that in [1]. In addition, the difference between Algorithm 2.1 and the algorithm in [1] exists in the calculation of the predictor step. Comparing with the results in [1],the global and local convergence of the two methods can be obtained under very mild conditions. The global convergence of the two methods do not need the boundness of the inverse of the Jacobian. The superlinear convergence of Algorithm 2.1‘ is obtained under the assumption of nonsingularity of generalized Jacobian of Φ(x,y) at the limit point and Algorithm 2.1 obtains superlinear convergence under the assumption of strict complementarity at the solution. The efficiency of the two methods is tested by numerical experiments. 相似文献
9.
非线性偏微分方程的约化和精确解 总被引:3,自引:0,他引:3
§ 1 IntroductionSeeking the exact solutions of the nonlinear partial differential equation is one of thevery importantsubjectin PDE research.Up to now,many methods offinding the exact so-lutions for NLPDE are constructed,such as inverse scattering transformation(IST) [1 ] ,Liepoint symmetry and similar reductions[2 ,3] ,B cklund[4— 6] and Cole-Hofe transformations,Hirota s bilinear method[7] ,the homogeneous balance method[8,9] ,tanh function method[1 0 ]and so on.In this paper,we giv… 相似文献
10.
§ 1.Introduction By a“meromorphic function” we mean a function that is meromorphic in the wholecomplex plane.It is assumed that the reader is familiar with notations of Nevanlinnatheory such as T(r,f) ,m(r,f) ,N (r,1f) ,S(r,f ) and so on that can be found,forinstance,in[1 ] or[2 ] .Let f and g be two meromorphic functions and a be a complexnumber. We say that f and g share the value a CM (counting multiplicity) if f -a andg-a have the same zeros with the same multiplicity,and denote th… 相似文献
11.
Zhi-congLiu Bei-yeFeng 《应用数学学报(英文版)》2004,20(4):573-578
In this paper, we give a rigorous mathematical and complete parameter analysis for the rheodynamic model of cardiac and obtain the conditions and parameter region for global existence and uniqueness of limit cycle and the global bifurcation diagram of limit cycles. We also discuss the resonance phenomenons of the perturbed system. 相似文献
12.
By the variable transformation and generalized Hirota method, exact homoclinic and heteroclinic solutions for Davey-Stewartson II (DSII) equation are obtained. For perturbed DSII equation, the existence of a global attractor is proved. The persistence of homoclinic and heteroclinic flows is investigated, and the special homoclinic and heteroclinic structure in attractors is shown. 相似文献
13.
§ 1 IntroductionInthispaperwediscusstheglobalclassicalsolutionofamultidimensionalquasistationaryproblem .Theproblemcomesfromthediscussionofagrowthmodelofselfmaintainingprotocell(see [1— 3])inmultidimensionalcase .Theprotocellcanbevisualizedashavingaporousst… 相似文献
14.
Tracial Limit of C^*-algebras 总被引:4,自引:0,他引:4
ShanWenHU HuaXinLIN YiFengXUE 《数学学报(英文版)》2003,19(3):535-556
A new limit of C^*-algebras, the tracial limit, is introduced in this paper. We show that a separable simple C^*-algebra A is a tracial limit of C^*-algebras in Z-(k) if and only if A has tracial topological rank no more than k. We present several known results using the notion of tracial limits. 相似文献
15.
WANGYOUBIN ZHAOAIMIN YANJURANG 《高校应用数学学报(英文版)》1998,13(4):391-396
The necessary and sufficient conditions for the oscillations of every solution of the nonlinear delay equation x(t) f(x(t l)) g(x([t-k]))=0 are oblained. 相似文献
16.
This paper discusses the global convergence of a class of nonmonotone conjugate gradient methods (NM methods) for nonconvex object functions. This class of methods includes the nonmonotone counterpart of modified Polak-Ribiere method and modified Hestenes-Stiefel method as special cases. 相似文献
17.
ZhangXiaodong LiJiongsheng WangPing 《高校应用数学学报(英文版)》1999,14(2):197-202
The Merris‘ conjectures for threshold graphs and d-regular graphs are proved. Andthe one of the conjectures of Merris holds for trees is also proved. 相似文献
18.
Suppose that there are two nonparametric populations x and y with missing data on both of them. We are interested in constructing confidence intervals on the quantile differences of
x and y. Random imputation is used. Empirical likelihood confidence intervals on the differences are constructed.
Supported by the National Natural Science Foundation of China (No. 10661003) and Natural Science Foundation of Guangxi (No.
0728092). 相似文献
19.
WANGGUOZHONG 《高校应用数学学报(英文版)》1996,11(1):85-100
Abstract. In this paper, a new iterated function system consisting of non-linear affine maps is constructed. We investigate the fractal interpolation functions generated by such a system and get its differentiabillty, its box dimension, its packing dimension,and a lower bound of its Hausdorff dimension. 相似文献
20.
In this paper, we give an explicit expression of the fundamental solutions and the global solvability for a class of LPDO's
consisting of left invariant vector fields on the nilpotent Lie groupG
d
1+d
2.
Supported by the National Postdoctoral Foundation.
Supported by the National Natural Science Foundation. 相似文献