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25 March 1998, Volume 18 Issue 1 Previous Issue    Next Issue

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GLOBAL EXISTENCE OF SOLUTIONS FOR A STRONGLY COUPLED REACTION-DIFFUSION SYSTEM Jiang Chengshun, Li Haifeng Acta mathematica scientia,Series B. 1998, 18 (1):  1-10.  Abstract ( 51 )   RICH HTML PDF (612KB) ( 33 )   Save This paper is concerned with an Initial Boundary Value Problem (IBVP) for a strongly coupled semilinear reaction-diffusion system. By using the upper and lower solutions method and Leray-Schauder fixed point theorem and so on, the authors prove the global eaistence and uniqueness of a smooth solution for this IBVP under some appropriate conditions. Related Articles | Metrics

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CONVERGENCE ANALYSIS ON A CLASS OF CONJUGATE GRADIENT METHODS WITHOUT SUFFICIENT DECREASE CONDITION Liu Gnanghui, Han Jiye, Qi Honduo, Xu Zhongling Acta mathematica scientia,Series B. 1998, 18 (1):  11-16.  Abstract ( 49 )   RICH HTML PDF (352KB) ( 42 )   Save Recently, Gilbert and Nocedal[3] investigated global convergence of conjugate gradient methods related to Polak-Ribiere formular, they restricted βK to non-negative value.[5] discussed the same problem as that in[3] and relaxed oh to be negative with the objective function being convex. This paper allows βK to be selected in a wider range than[5]. Especially, the global convergence of the corresponding algorithm without sufficient decrease condition is proved. Related Articles | Metrics

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THE ANALYTIC KREIN-MILMAN PROPERTY IN BANACH SPACES Bu Shangquan Acta mathematica scientia,Series B. 1998, 18 (1):  17-24.  Abstract ( 58 )   RICH HTML PDF (516KB) ( 32 )   Save In the papaer, it is defined the analytic Krein-Milman property for plurisubharmonic convex subsets in complex Banach spaces and studied the relation between it and the analytic Radon-Nikodym property. Related Articles | Metrics

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ON THE CAUCHY PROBLEM OF THE KURAMOTO-SIVASHINSKY EQUATION WITH SINGULAR INITIAL DATA Zhao Huijiang, Liu Zaihua, Chen Shiping Acta mathematica scientia,Series B. 1998, 18 (1):  25-34.  Abstract ( 52 )   RICH HTML PDF (587KB) ( 36 )   Save In this paper, it is considered that the global existence, uniqueness and regularity results for the Cauchy problem of the well-known Kuramoto-Stvashinsky equation ut+1/2▽(|u|2)+△u+△2u=0,t>0,x∈RN, u(0,x)=u0(x),x∈RN. only under the condition u0(x) ∈L2(RN, Rn). Where u(t, x)=(u1 (t, x),…,un (t, x))T is the unknown vector-valued function. Results show that for N < 6,u0 (x) ∈L2 (RN, Rn), the above Cauchy problem admits a unique global solution u(t, z) which belongs to C∞,∞ (RN×(0, ∞)). Related Articles | Metrics

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ON THE ASYMPTOTIC ORDER OF TIKHONOV REGULARIZATION WITH OPERATORS AND DATA ERROR Chen Hong Acta mathematica scientia,Series B. 1998, 18 (1):  35-44.  Abstract ( 37 )   RICH HTML PDF (554KB) ( 37 )   Save It is considered that the Tikhonov regularization with closed operators for solving linear OPerator equations of the first kind in the presence of perturbed operators. A class of the regularization parameter choice strategies that lead to optimal convergence rates are proposed. Related Articles | Metrics

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THE RIEMANN PROBLEM FOR A TWO-DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS WITH NON-CLASSICAL SHOCK WAVES Hu Jiaxin Acta mathematica scientia,Series B. 1998, 18 (1):  45-56.  Abstract ( 40 )   RICH HTML PDF (645KB) ( 35 )   Save The Riemann problem for a two-dimensional 2×2 nonstrictly hyperbolic system of nonlinear conservaion laws has been solved thoroughly for any gived initial data which are constant in each quadrant. The non-classical shock waves, which are labelled as δ-shock waves, appear in some solutions. The solutions have been obtained are hot unique. Due to the specific property of the system considered, there are no rarefaction waves in solution.This paper is divided into three parts. The first part constructs Riemann solutions for initial data involving two contact discontinuities while the second considers the case for other initial data. The last part briefly discusses the non-uniqueness of the solutions. Related Articles | Metrics

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ASYMPTOTIC BEHMIOUR IN A REACTION-DIFFUSION SYSTEM Huang Shuxiang, Xie Chunhong Acta mathematica scientia,Series B. 1998, 18 (1):  57-62.  Abstract ( 31 )   RICH HTML PDF (382KB) ( 34 )   Save This paper proves the asymptotic behaviour for a class of reaction-diffusion system in bacteriology by using duality technique, semigroup theorem, Lp-estimates and upper and lower solutions method. Related Articles | Metrics

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HOLOMORPHIC INTERGATED MILD C-EXISTENCE FAMILIES Gao Mingchu Acta mathematica scientia,Series B. 1998, 18 (1):  63-73.  Abstract ( 44 )   RICH HTML PDF (700KB) ( 39 )   Save By defined holomorphic n-times integrated mild C-existence families and C-semigroups, their relationship with holomorphic mild C1-exustence families and holomorphic C1 -semigroups is discussed, respectively. For exponentially bounded cases, this paper gives several Hille-Yosida type conditions for an operator to have (or generate) one of these families of operators and generalize the corresponding results in[1],[2] and[3]. These families by the holomorphic solvability of the abstract Cauchy problem is also characterized. Related Articles | Metrics

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ON THE PERIODIC ORTHONORMAL WAVELET SYSTEM Dai Daoqing, Lin Wei Acta mathematica scientia,Series B. 1998, 18 (1):  74-78.  Abstract ( 48 )   RICH HTML PDF (287KB) ( 31 )   Save This paper concerns with the point-wise convergence of a wavelet series for Lp functions and the characterization of Holder class by both the partial sums approximation and the best approximation. Related Articles | Metrics

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EQUILIBIA OF NONCOMPACT GENERALIZED GAMES WITH CORRESPONDENCES WITHOUT OPEN LOWER SECTIONS Ding Xieping Acta mathematica scientia,Series B. 1998, 18 (1):  79-89.  Abstract ( 35 )   RICH HTML PDF (704KB) ( 39 )   Save The new classes of LFc-correspondences and LFc -majorised correspondences without open lower sections is introduced. Some existence theorems of madximal elements of the LFc -correspondences and the LFc-majorized correspondences defined on noncompact set in topological vector spaces are obtained. As applications, some existence theorems of equilibrium points for one-person games, qualitative games and generalized games with the LFc -majorized correspondences devined on noncompact strategy sets in topological vector spaces are also given. These theorems improve and generalize several known results in recent literature. Related Articles | Metrics

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ON THE COMPARISON THEOREM OF THE GTOR METHOD Li Wen Acta mathematica scientia,Series B. 1998, 18 (1):  90-94.  Abstract ( 31 )   RICH HTML PDF (338KB) ( 31 )   Save This paper presents a comparison theorem of the generalized TOR method for solving linear systems. By applying this theorem, some recent results are derived. Related Articles | Metrics

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OSCILLATORY AND ASYMPTOTIC BEHMIOUR OF A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS OF THIRD ORDER N. Parhi, P. Das Acta mathematica scientia,Series B. 1998, 18 (1):  95-106.  Abstract ( 50 )   RICH HTML PDF (721KB) ( 31 )   Save This paper deals with oscillatory/nonoscillatory behaviour of solutions of third order nonlinear differential equations of the form y"'+a(t)y"+b(t)y'+c(t)yr=0 (1) and y"'+a(t)y"+b(t)y'+c(t)f(y)=0,(2) where a,b,c ∈ C([σ,∞),R) such that a(t) does not change sign, b(t) ≤ 0, c(t) > 0,f∈C(R, R) such that (f(y)/y) ≥ β > 0 for y ≠ 0 and γ > 0 is a quotient of odd integers.It has been shown, under certain conditions on coefficient functions, that a solution of (1) and (2) which Las a zero is oscillatory and the nonoscillatory solutions of these equations tend to zero as t → ∞. The motivation for this work came from the observation that the equation u"'+ay"+by'+cy=0,(3) where a, b, c are constants such that b ≤ 0, c > 0, has an oscillatory solution if (2a3)/27-ab/3+c-2/3γ3(a2/3-b)3/2>0 and only ifand all nonoscillatory solutions of (3) tend to zero if and only if the equation has an oscillatory solution. Related Articles | Metrics

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BOUNDS FOR SOLUTIONS OF A THREE-POINT PARTIAL DIFFERENCE EQUATION Lin Yizhong, Suisun Cheng Acta mathematica scientia,Series B. 1998, 18 (1):  107-112.  Abstract ( 52 )   RICH HTML PDF (314KB) ( 34 )   Save This paper is concerned with a class of partial difference equations with variable coefficients. Explicit growth bounds are found for their solutions. These bounds provide information on the existence of exponentially bounded solutions. Related Articles | Metrics

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BOUNDEDNESS OF SOLUTIONS AND EXISTENCE OF LIMIT CYCLES FOR A NONLINEAR SYSTEM OF DIFFERENTIAL EQUATIONS Huang Lihong, Chen Mingpo Acta mathematica scientia,Series B. 1998, 18 (1):  113-120.  Abstract ( 30 )   RICH HTML PDF (491KB) ( 30 )   Save In this paper, author obtain sufficient conditions for the boundedness of solutions and the existence of limit cycles of the nonlinear differential system dx/dt=p(y),dy/dt=-q(y)h(x,y)-g(x) without the traditional assumptions "h(x, y) ≥ 0 for|x|sufficiently large" and "∫0±∞ g (x)dx=+∞". Related Articles | Metrics