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2013年, 第33卷, 第1期　刊出日期：2013-01-20 上一期    下一期

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ON DECOMPOSITION METHOD FOR ACOUSTIC WAVE SCATTERING BY MULTIPLE OBSTACLES 王海兵, 刘继军 数学物理学报(英文版). 2013 (1):  1-22.  DOI: 10.1016/S0252-9602(12)60191-X 摘要 ( 864 )   RICH HTML PDF(487KB) ( 1177 )   收藏 Consider acoustic wave scattering by multiple obstacles with different sound properties on the boundary, which can be modeled by a mixed boundary value problem for the Helmholtz equation in frequency domain. Compared with the standard scattering problem for one obstacle, the difficulty of such a new problem is the interaction of scattered wave by different obstacles. A decomposition method for solving this multiple scattering problem is developed. Using the boundary integral equation method, we decompose the total scattered field into a sum of contributions by separated obstacles. Each contribution corresponds to scattering problem of single obstacle. However, all the single scattering problems are coupled via the boundary conditions, representing the physical interaction of scattered wave by different obstacles. We prove the feasibility of such a decomposition. To compute these contributions efficiently, an iteration algorithm of Jacobi type is proposed, decoupling the interaction of scattered wave from the numerical points of view. Under the well-separation assumptions on multiple obstacles, we prove the convergence of iteration sequence generated by the Jacobi algorithm, and give the error estimate between exact scattered wave and the iteration solution in terms of the obstacle size and the minimal distance of multiple obstacles. Such a quantitative description reveals the essences of wave scattering by multiple obstacles. Numerical examples showing the accuracy and convergence of our method are presented. 参考文献 | 相关文章 | 计量指标

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GENERAL DECAY FOR A POROUS-THERMOELASTIC SYSTEM WITH MEMORY: THE CASE OF NONEQUAL SPEEDS Salim A. MESSAOUDI, Abdelfeteh FAREH 数学物理学报(英文版). 2013 (1):  23-40.  DOI: 10.1016/S0252-9602(12)60192-1 摘要 ( 527 )   RICH HTML PDF(196KB) ( 1163 )   收藏 The aim of this paper is to establish a general decay result for a one-dimensional porous elastic system with different speeds of wave propagation in the presence of macrotem-perature effect and visco-porous dissipation. 参考文献 | 相关文章 | 计量指标

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GLOBAL EXISTENCE, UNIFORM DECAY AND EXPONENTIAL GROWTH FOR A CLASS OF SEMI-LINEAR WAVE EQUATION WITH STRONG DAMPING 陈化, 刘功伟 数学物理学报(英文版). 2013 (1):  41-58.  DOI: 10.1016/S0252-9602(12)60193-3 摘要 ( 665 )   RICH HTML PDF(226KB) ( 929 )   收藏 In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 < E(0) < d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E(0) < 0. 参考文献 | 相关文章 | 计量指标

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SOME SHARP RELLICH TYPE INEQUALITIES ON NILPOTENT GROUPS AND APPLICATION 连保胜 数学物理学报(英文版). 2013 (1):  59-74.  DOI: 10.1016/S0252-9602(12)60194-5 摘要 ( 447 )   RICH HTML PDF(203KB) ( 939 )   收藏 We prove some Rellich type inequalities for the sub-Laplacian on Carnot nilpotent groups. Using the same method, we obtain some analogous inequalities for the Heisenberg-Greiner operators. In most cases, the constants we obtained are optimal. 参考文献 | 相关文章 | 计量指标

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LOCAL STABILITY OF TRAVELLING FRONTS FOR A DAMPED WAVE EQUATION 罗操 数学物理学报(英文版). 2013 (1):  75-83.  DOI: 10.1016/S0252-9602(12)60195-7 摘要 ( 459 )   RICH HTML PDF(179KB) ( 1018 )   收藏 The paper is concerned with the long-time behaviour of the travelling fronts of the damped wave equation ∂utt+ut = uxx−V ′(u) on R. The long-time asymptotics of the solutions of this equation are quite similar to those of the corresponding reaction-diffusion equation ut = uxx − V ′(u). Whereas a lot is known about the local stability of travelling fronts in parabolic systems, for the hyperbolic equations it is only briefly discussed when the potential V is of bistable type. However, for the combustion or monostable type of V , the problem is much more complicated. In this paper, a local stability result for travelling fronts of this equation with combustion type of nonlinearity is established. And then, the result is extended to the damped wave equation with a case of monostable pushed front. 参考文献 | 相关文章 | 计量指标

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ELASTIC MEMBRANE EQUATION WITH MEMORY TERM AND NONLINEAR BOUNDARY DAMPING: GLOBAL EXISTENCE, DECAY AND BLOWUP OF THE SOLUTION Abderrahmane ZARAI, Nasser-eddine TATAR, Salem ABDELMALEK 数学物理学报(英文版). 2013 (1):  84-106.  DOI: 10.1016/S0252-9602(12)60196-9 摘要 ( 760 )   RICH HTML PDF(231KB) ( 1138 )   收藏 In this paper we consider the Elastic membrane equation with memory term and nonlinear boundary damping. Under some appropriate assumptions on the relaxation function h and with certain initial data, the global existence of solutions and a general decay for the energy are established using the multiplier technique. Also, we show that a nonlinear source of polynomial type is able to force solutions to blow up in finite time even in presence of a nonlinear damping. 参考文献 | 相关文章 | 计量指标

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EXISTENCE OF MULTIPLE SOLUTIONS FOR SINGULAR QUASILINEAR ELLIPTIC SYSTEM WITH CRITICAL SOBOLEV-HARDY EXPONENTS AND CONCAVE-CONVEX TERMS 李圆晓, 高文杰 数学物理学报(英文版). 2013 (1):  107-121.  DOI: 10.1016/S0252-9602(12)60197-0 摘要 ( 462 )   RICH HTML PDF(217KB) ( 924 )   收藏 The main purpose of this paper is to establish the existence of multiple so-lutions for singular elliptic system involving the critical Sobolev-Hardy exponents and concave-convex nonlinearities. It is shown, by means of variational methods, that under certain conditions, the system has at least two positive solutions. 参考文献 | 相关文章 | 计量指标

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UNIQUENESS PROBLEM FOR MEROMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES INTO PN(C) WITH TRUNCATED MULTIPLICITIES 涂振汉, 王中华 数学物理学报(英文版). 2013 (1):  122-130.  DOI: 10.1016/S0252-9602(12)60198-2 摘要 ( 571 )   RICH HTML PDF(159KB) ( 753 )   收藏 This paper proves some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space PN(C) with truncated multi-plicities, and our results improve some earlier work. 参考文献 | 相关文章 | 计量指标

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FINITE p-GROUPS WHICH CONTAIN A SELF-CENTRALIZING CYCLIC NORMAL SUBGROUP 郝成功, 靳竹萱 数学物理学报(英文版). 2013 (1):  131-138.  DOI: 10.1016/S0252-9602(12)60199-4 摘要 ( 377 )   RICH HTML PDF(159KB) ( 1094 )   收藏 For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applica-tions are given, including a character theoretic description for such groups. 参考文献 | 相关文章 | 计量指标

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THE SIMULTANEOUS AND NON-SIMULTANEOUS BLOW-UP CRITERIA FOR A DIFFUSION SYSTEM 凌征球*, 王泽佳, 张国强 数学物理学报(英文版). 2013 (1):  139-149.  DOI: 10.1016/S0252-9602(12)60200-8 摘要 ( 494 )   RICH HTML PDF(176KB) ( 826 )   收藏 This paper investigates the finite time blow-up of nonnegative solutions for a nonlinear diffusion system with a more complicated source term, which is a product of localized source, local source, and weight function, and complemented by homogeneous Dirichlet boundary conditions. The criteria are proposed to identify simultaneous and non-simultaneous blow-up solutions. Moreover, the related classification for the four parameters in the model is optimal and complete. The results extend those in Zhang and Yang [12]. 参考文献 | 相关文章 | 计量指标

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A LITTLEWOOD-PALEY TYPE THEOREM FOR BERGMAN SPACES 陈泽乾, 欧阳威 数学物理学报(英文版). 2013 (1):  150-154.  DOI: 10.1016/S0252-9602(12)60201-X 摘要 ( 478 )   RICH HTML PDF(139KB) ( 806 )   收藏 In this paper, we prove that the original Littlewood-Paley g-functions can be used to characterize Bergman spaces as well. 参考文献 | 相关文章 | 计量指标

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EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A CLASS OF p(x)-BIHARMONIC EQUATIONS 李麟, 唐春雷 数学物理学报(英文版). 2013 (1):  155-170.  DOI: 10.1016/S0252-9602(12)60202-1 摘要 ( 471 )   RICH HTML PDF(226KB) ( 1576 )   收藏 In this paper, we study a class of p(x)-biharmonic equations with Navier boundary condition. Using the mountain pass theorem, fountain theorem, local linking theorem and symmetric mountain pass theorem, we establish the existence of at least one solution and infinitely many solutions of this problem, respectively. 参考文献 | 相关文章 | 计量指标

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SOME EXTENSIONS OF THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS 吴加勇 数学物理学报(英文版). 2013 (1):  171-186.  DOI: 10.1016/S0252-9602(12)60203-3 摘要 ( 625 )   RICH HTML PDF(215KB) ( 980 )   收藏 Given a family of smooth immersions of closed hypersurfaces in a locally sym-metric Riemannian manifold with bounded geometry, moving by mean curvature flow, we show that at the first finite singular time of mean curvature flow, certain subcritical quan-tities concerning the second fundamental form blow up. This result not only generalizes a result of Le-Sesum and Xu-Ye-Zhao, but also extends the latest work of Le in the Euclidean case. 参考文献 | 相关文章 | 计量指标

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ON CLASSES OF REGULAR GRAPHS WITH CONSTANT METRIC DIMENSION Muhammad IMRAN, Syed Ahtsham ul Haq BOKHARY, Ali AHMAD, Andrea SEMANICOVá-FE?OVCíKOVá 数学物理学报(英文版). 2013 (1):  187-206.  DOI: 10.1016/S0252-9602(12)60204-5 摘要 ( 464 )   RICH HTML PDF(234KB) ( 2016 )   收藏 In this paper, we are dealing with the study of the metric dimension of some classes of regular graphs by considering a class of bridgeless cubic graphs called the flower snarks Jn, a class of cubic convex polytopes considering the open problem raised in [M. Imran et al., families of plane graphs with constant metric dimension, Utilitas Math., in press] and finally Harary graphs H5,n by partially answering to an open problem proposed in [I. Javaid et al., Families of regular graphs with constant metric dimension, Utilitas Math., 2012, 88: 43–57]. We prove that these classes of regular graphs have constant metric dimension. 参考文献 | 相关文章 | 计量指标

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LOCAL ANALYTIC SOLUTIONS OF A MORE GENERALIZED DHOMBRES EQUATION 张倩 数学物理学报(英文版). 2013 (1):  207-217.  DOI: 10.1016/S0252-9602(12)60205-7 摘要 ( 398 )   RICH HTML PDF(180KB) ( 724 )   收藏 We study the local analytic solutions f of the functional equation f( Ψ(zf(z))) =φ(f(z)) for z in some neighborhood of the origin. Whether the solution f vanishes at z = 0 or not plays a critical role for local analytic solutions of this equation. In this paper, we obtain results of analytic solutions not only in the case f(0) = 0 but also for f(0) 6= 0. When assuming f(0) = 0, for technical reasons, we just get the result for f′(0) ≠ 0. Then when assuming f(0) =ω0 ≠ 0,  Ψ′(0) = s ≠ 0,  (z) is analytic at z = 0 and φ'(z) is analytic at z =ω0, we give the existence of local analytic solutions f in the case of 0 < |sω0| < 1 and the case of |sω0| = 1 with the Brjuno condition. 参考文献 | 相关文章 | 计量指标

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OSCILLATORY BEHAVIOR OF SOLUTIONS OF CERTAIN THIRD ORDER MIXED NEUTRAL DIFFERENCE EQUATIONS E. THANDAPANI, N. KAVITHA 数学物理学报(英文版). 2013 (1):  218-226.  DOI: 10.1016/S0252-9602(12)60206-9 摘要 ( 446 )   RICH HTML PDF(158KB) ( 1006 )   收藏 The objective of this paper is to study the oscillatory and asymptotic prop-erties of the mixed type third order neutral difference equation of the form Δ(anΔ2 (xn + bnxn−τ1 + cnxn+τ2 ))+ qnxβn+1−σ1 pnxβn+1+σ2= 0, where {an} , {bn} , {cn} , {qn} and {pn} are positive real sequences, β is a ratio of odd positive integers, τ1, τ2, σ1 and σ2 are positive integers. We establish some sufficient conditions which ensure that all solutions are either oscillatory or converges to zero. Some examples are presented to illustrate the main results. 参考文献 | 相关文章 | 计量指标

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PATHS AND CYCLES EMBEDDING ON FAULTY ENHANCED HYPERCUBE NETWORKS 刘敏, 刘红美 数学物理学报(英文版). 2013 (1):  227-246.  DOI: 10.1016/S0252-9602(12)60207-0 摘要 ( 463 )   RICH HTML PDF(291KB) ( 1090 )   收藏 Let Qn,k (n ≥ 3, 1≤ k≤ n − 1) be an n-dimensional enhanced hypercube which is an attractive variant of the hypercube and can be obtained by adding some com-plementary edges, fv and fe be the numbers of faulty vertices and faulty edges, respectively. In this paper, we give three main results. First, a fault-free path P[u, v] of length at least 2n−2fv−1 (respectively, 2n−2fv−2) can be embedded on Qn,k with fv+fe ≤ n−1 when dQn,k (u, v) is odd (respectively, dQn,k (u, v) is even). Secondly, an Qn,k is (n − 2) edge-fault-free hyper Hamiltonian-laceable when n (≥ 3) and k have the same parity. Lastly, a fault-free cycle of length at least 2n − 2fv can be embedded on Qn,k with fe ≤ n − 1 and fv + fe ≤ 2n − 4. 参考文献 | 相关文章 | 计量指标

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THE GLOBAL L2 STABILITY OF SOLUTIONS TO THREE DIMENSIONAL MHD EQUATIONS 李现金, 蔡晓静 数学物理学报(英文版). 2013 (1):  247-267.  DOI: 10.1016/S0252-9602(12)60208-2 摘要 ( 648 )   RICH HTML PDF(218KB) ( 692 )   收藏 In this paper, we mainly study the global L2 stability for large solutions to the MHD equations in three-dimensional bounded or unbounded domains. Under suitable conditions of the large solutions, it is shown that the large solutions are stable. And we obtain the equivalent condition of this stability condition. Moreover, the global existence and the stability of two-dimensional MHD equations under three-dimensional perturbations are also established. 参考文献 | 相关文章 | 计量指标

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ON THE SHARING VALUES OF ALGEBROID FUNCTIONS AND THEIR DERIVATIVES 刘慧芳, 孙道椿 数学物理学报(英文版). 2013 (1):  268-278.  DOI: 10.1016/S0252-9602(12)60209-4 摘要 ( 688 )   RICH HTML PDF(166KB) ( 935 )   收藏 In this paper, we define the shared value of an algebroid function and its derivative on its Riemann surface. By considering the relationship between the shared values and the branch points of algebroid functions and their derivatives, we obtain some uniqueness theorems of algebroid functions sharing values with their derivatives, which ex-tend 3 IM shared values theorem of nonconstant meromorphic functions and their deriva-tives obtained by Mues-Steinmetz and Gundersen. 参考文献 | 相关文章 | 计量指标

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TWO-DIMENSIONAL MAXIMAL OPERATOR OF DYADIC DERIVATIVE ON VILENKIN MARTINGALE SPACES 张传洲, 张学英 数学物理学报(英文版). 2013 (1):  279-289.  DOI: 10.1016/S0252-9602(12)60210-0 摘要 ( 406 )   RICH HTML PDF(179KB) ( 775 )   收藏 In [1] the boundedness of one dimensional maximal operator of dyadic deriva-tive is discussed. In this paper, we consider the two-dimensional maximal operator of dyadic derivative on Vilenkin martingale spaces. With the help of counter-example we prove that the maximal operator is not bounded from the Hardy space Hq to the Hardy space Hq for 0 < q ≤ 1 and is bounded from p∑α , Dα to Lα for some α. 参考文献 | 相关文章 | 计量指标

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EXISTENCE AND ATTRACTIVITY OF k-ALMOST AUTOMORPHIC SEQUENCE SOLUTION OF A MODEL OF CELLULAR NEURAL NETWORKS WITH DELAY Syed ABBAS, 夏永辉 数学物理学报(英文版). 2013 (1):  290-302.  DOI: 10.1016/S0252-9602(12)60211-2 摘要 ( 489 )   RICH HTML PDF(181KB) ( 1038 )   收藏 In this paper we discuss the existence and global attractivity of k-almost au-tomorphic sequence solution of a model of cellular neural networks. We consider the cor-responding difference equation analogue of the model system using suitable discretization method and obtain certain conditions for the existence of solution. Almost automorphic function is a good generalization of almost periodic function. This is the first paper con-sidering such solutions of the neural networks. 参考文献 | 相关文章 | 计量指标

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WEAK CONVERGENCE THEOREMS FOR GENERAL EQUILIBRIUM PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEMS IN BANACH SPACES 蔡钢, 步尚全 数学物理学报(英文版). 2013 (1):  303-320.  DOI: 10.1016/S0252-9602(12)60212-4 摘要 ( 436 )   RICH HTML PDF(218KB) ( 1086 )   收藏 In this paper, we introduce two new iterative algorithms for finding a common element of the set of solutions of a general equilibrium problem and the set of solutions of the variational inequality for an inverse-strongly monotone operator and the set of common fixed points of two infinite families of relatively nonexpansive mappings or the set of common fixed points of an infinite family of relatively quasi-nonexpansive mappings in Banach spaces. Then we study the weak convergence of the two iterative sequences. Our results improve and extend the results announced by many others. 参考文献 | 相关文章 | 计量指标