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1.
The authors study homogenization of some nonlinear partial differential equations of theform-div(a(hx,h~2x,Du_h))=f,where a is periodic in the first two arguments and monotonein the third.In particular the case where a satisfies degenerated structure conditions is studied.It is proved that u_h converges weakly in W_0~(1,1)(Ω)to the unique solution of a limit problem ash→∞.Moreover,explicit expressions for the limit problem are obtained. 相似文献
2.
61. IntroductionLet us consider the clajss of partial differential equations of the form--div(a.(x, Du.)) ~ f on fi, us E Wt,p(fl), (1.1)where a6 is increasingly oscillating as E -- 0, fi is an open bounded subset of R", 1 < p < cot1/p 1/q = 1 and f E W--"q(fl). The homogenization problem for (l.1) consists of the studyof the asymptotic behavior of solutions net as e - 0. In many important cases nE convergesweakly in WI'p(n) to the solution no of the homogenized problem--div(b(Duo)) = f … 相似文献
3.
Nikolaos S. PAPAGEORGIOU Nikolaos YANNAKAKIS 《数学学报(英文版)》2005,21(5):977-996
This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x(t) and x(t). In this first part we prove existence and relaxation theorems. We consider the case of an usc, convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C^1 (T, H). Also we examine the Isc, nonconvex case and again we prove the existence of solutions. In addition we establish the existence of extremal solutions and by strengthening our hypotheses, we show that the extremal solutions are dense in C^1 (T, H) to the solutions of the original convex problem (strong relaxation). An example of a nonlinear hyperbolic optimal control problem is also discussed. 相似文献
4.
关于单调变分不等式的不精确邻近点算法的收敛性分析 总被引:7,自引:0,他引:7
王治华 《高等学校计算数学学报》2003,25(4):336-343
We consider a proximal point algorithm(PPA) for solving monotone variational inequalities. PPA generates a sequence by solving a sequence of strongly monotone subproblems .However,solving the subproblems is either expensive or impossible. Some inexact proximal point algorithms(IPPA) have been developed in many literatures. In this paper, we present a criterion for approximately solving subproblems. It only needs one simple additional work on the basis of original algorithm, and the convergence criterion becomes milder. We show that this method converges globally under new criterion provided that the solution set of the problem is nonempty. 相似文献
5.
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
6.
In this paper we introduce two sequences of operator functions and their dual functions:f_k(t)=((tlog t)~k-(t-1)~k)/(log~k 1t)(k=1,2,...),gk(t)=((t-1)~k-log~k t)/(log~k 1t)(k=1,2,...)and f_k~*=(t~klog~(k 1)t)/((tlog t)~k-(t-1)~k)(k=1,2,...),g_k~*(t)=(t~klog~(k 1)t)/((t-1)~k-log~k t)(k=1,2,...)definedon(0, ∞). We find that they are all operator monotone functions with respect to the strictly chaotic order and some ordinary orders among positive invertible operators.Indeed,we extend the results of the operator monotone function(tlog t -t 1)/(log~2t)which is widely used in the theory of heat transfer of the heat engineering and fluid mechanics[1]. 相似文献
7.
The value of a European option satisfies the Black-Scholes equation with appropriately specified final and boundary conditions.We transform the problem to an initial boundary value problem in dimensionless form.There are two parameters in the coefficients of the resulting linear parabolic partial differential equation.For a range of values of these parameters,the solution of the problem has a boundary or an initial layer.The initial function has a discontinuity in the first-order derivative,which leads to the appearance of an interior layer.We construct analytically the asymptotic solution of the equation in a finite domain.Based on the asymptotic solution we can determine the size of the artificial boundary such that the required solution in a finite domain in x and at the final time is not affected by the boundary.Also,we study computationally the behaviour in the maximum norm of the errors in numerical solutions in cases such that one of the parameters varies from finite (or pretty large) to small values,while the other parameter is fixed and takes either finite (or pretty large) or small values. Crank-Nicolson explicit and implicit schemes using centered or upwind approximations to the derivative are studied.We present numerical computations,which determine experimentally the parameter-uniform rates of convergence.We note that this rate is rather weak,due probably to mixed sources of error such as initial and boundary layers and the discontinuity in the derivative of the solution. 相似文献
8.
吴正昌 《高校应用数学学报(英文版)》2002,17(3):291-300
Shifts-invariant spaces in L1 (R) are investigated. First,based on a study of the system of linearly difference operators, the method of constructing generators with linearly independent shifts is provided. Then the characterizations of the closed shift-invariant subspaces in L1 (R) are given in terms of such generators and the local basis of shift-invariant subspaces. 相似文献
9.
Hongmei Shao Wei Wu Wenbin Liu 《高等学校计算数学学报(英文版)》2007,16(3):193-202
The capability of multilayer perceptrons(MLPs)for approximating continuous functions with arbitrary accuracy has been demonstrated in the past decades.Back propagation(BP)algorithm is the most popular learning algorithm for training of MLPs.In this paper,a simple iteration formula is used to select the leaming rate for each cycle of training procedure,and a convergence result is presented for the BP algo- rithm for training MLP with a hidden layer and a linear output unit.The monotonicity of the error function is also guaranteed during the training iteration. 相似文献
10.
A.Al-Shuaibi F.Al-Rawjih 《分析论及其应用》2004,20(1):28-34
Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated. 相似文献
11.
ZHANG Fei-ran ZHOU Xiao-zhong. Department of Mathematics Shangqiu Teacher''''s College Shangqiu China . Department of Print Engineering the Advanced College of Shanghai Publishing Print Shanghai China 《数学季刊》2004,19(1):69-74
By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A1+A2, B=B1+B2,A1 and B1 are mixed monotone, A2 and B2 are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations. 相似文献
12.
MichaelIosifGIL‘ 《数学学报(英文版)》2003,19(2):313-326
A class of pencils(operator-valued functions of a complex argument) in a separeble Hilbert space is considered.Bounds for the spectra are derived.Applications to differential operators,integral operators with delay and in finite matrix pencils are discussed. 相似文献
13.
In the present paper, we find that the Bemstein-Durrmeyer operators, besides their better applications in approximation theory and some other fields, are good tools in constructing translation network. With the help of the de la Vallee properties of the Bernstein-Durrmeyer operators a sequence of translation network operators is constructed and its degree of approximation is dealt. 相似文献
14.
Wen Ming WU Li Guang WANG 《数学学报(英文版)》2007,23(3):491-496
15.
EXISTENCE,MULTIPLICITY AND STABILITY RESULTS FOR POSITIVE SOLUTIONS OF NONLINEAR p-LAPLACIAN EQUATIONS 总被引:1,自引:0,他引:1 下载免费PDF全文
This paper studies the existence of positive solutions of the Dirichlet problem for the nonlinear equation involving p-Laplacian operator:-△pu=λf(u) on a bounded smooth domain Ω in Rn. The authors extend part of the Crandall-Rabinowitz bifurcation theory to this problem. Typical examples are checked in detail and multiplicity of the solutions are illustrated. Then the stability for the associated parabolic equation is considered and a Fujita-type result is presented. 相似文献
16.
Wang Yi Fan Yizheng Tan Yingying 《高校应用数学学报(英文版)》2007,22(4):478-484
In this paper,an equivalent condition of a graph G with t(2≤t≤n)distinct Laplacian eigenvalues is established.By applying this condition to t=3,if G is regular(neces- sarily be strongly regular),an equivalent condition of G being Laplacian integral is given.Also for the case of t=3,if G is non-regular,it is found that G has diameter 2 and girth at most 5 if G is not a tree.Graph G is characterized in the case of its being triangle-free,bipartite and pentagon-free.In both cases,G is Laplacian integral. 相似文献
17.
有关M.S.Berger问题的注记 总被引:1,自引:0,他引:1
In this paper, we discuss the problem concerning global and local structure of solutions of an operator equation posed by M. S. Berger. Let f : U 真包含 E → F be a C1 map, where E and F are Banach spaces and U is open in E. We show that the solution set of the equation f(x) = y for a fixed generalized regular value y of f is represented as a union of disjoint connected C1 Banach submanifolds of U, each of which has a dimension and its tangent space is given. In particular, a characterization of the isolated solutions of the equation f(x) = y is obtained. 相似文献
18.
ZengXiaoming LinLu 《数学研究》1994,27(1):200-203
In this paper ,a class of Bernstein-Trotter type operator and its limiting properties are studied. By using both the limiting theorem and P. Le‘ vy continuity theorem on probability theory, a theorem of convergence is obtained. The result in [1] is included. 相似文献
19.
On "Problems on von Neumann Algebras by R. Kadison, 1967" 总被引:1,自引:0,他引:1
LiMingGE 《数学学报(英文版)》2003,19(3):619-624
A brief summary of the development on Kadison‘s famous problems (1967) is given. A new set of problems in von Neumann algebras is listed. 相似文献
20.
In this paper, we prove that the norm closure of all linear combinations of two unitary operators is equal to the norm closure of all invertible operators in B(H). We apply the results to frame representations and give some simple and alternative proofs of the propositions in “P. G. Casazza, Every frame is a sum of three (but not two) orthonormal bases-and other frame representations, J. Fourier Anal. Appl., 4(6)(1998), 727-732.” 相似文献