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EXISTENCE OF SOLUTION FOR A BOUNDARY VALUE PROBLEM OF FRACTIONAL ORDER Zhang Shuqin Acta mathematica scientia,Series B    DOI: 10.1016/S0252-9602(06)60044-1

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ASYMPTOTIC STABILITY OF RAREFACTION WAVE FOR HYPERBOLIC-ELLIPTIC COUPLED SYSTEM IN RADIATING GAS Ruan Lizhi; Zhang Jing Acta mathematica scientia,Series B    DOI: 10.1016/S0252-9602(07)60035-6

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L2 DECAY OF THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DAMPING CAI Xiao-Jing, LEI Li-Hua Acta mathematica scientia,Series B    2010, 30 (4): 1235-1248.   DOI: 10.1016/S0252-9602(10)60120-8 Abstract （870）      PDF（pc） （194KB）（1589）       Save In this article, we show large time behavior of weak solutions to the Cauchy problem of the Navier-Stokes equations  with damping α|u|β-1u (α>0). Reference | Related Articles | Metrics

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EXACT NULL CONTROLLABILITY OF NON-AUTONOMOUS FUNCTIONAL EVOLUTION SYSTEMS WITH NONLOCAL CONDITIONS FU Xian-Long, ZHANG Yu Acta mathematica scientia,Series B    2013, 33 (3): 747-757.   DOI: 10.1016/S0252-9602(13)60035-1 Abstract （283）      PDF（pc） （178KB）（1128）       Save In this article, by using theory of linear evolution system and Schauder fixed point theorem, we establish a sufficient result of exact null controllability for a non-autonomous functional evolution system with nonlocal conditions. In particular, the compactness condi-tion or Lipschitz condition for the function g in the nonlocal conditions appearing in various literatures is not required here. An example is also provided to show an application of the obtained result. Reference | Related Articles | Metrics

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MULTIPLE SOLUTIONS FOR THE p&q-LAPLACIAN PROBLEM WITH CRITICAL EXPONENT LI Gong-Bao, ZHANG Guo Acta mathematica scientia,Series B    2009, 29 (4): 903-918.   DOI: 10.1016/S0252-9602(09)60077-1 Abstract （1027）      PDF（pc） （222KB）（2387）       Save In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p&q-Laplacian type involving the critical Sobolev exponent: −△pu − △qu = |u|p*−2u + μ|u|r−2u in Ω, u|∂Ω= 0, where Ω ⊂ RN is a bounded domain, N > p, p* = Np /N−p is the critical Sobolev exponent and μ > 0. We prove that if 1 < r < q < p < N, then there is a μ0 > 0, such that for any μ ∈ (0, μ0), the above mentioned problem possesses infinitely many weak solutions. Our result generalizes a similar result in [8] for p-Laplacian type problem. Reference | Related Articles | Metrics

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PROJECTIVELY FLAT MATSUMOTO METRIC AND ITS APPROXIMATION Li Benling Acta mathematica scientia,Series B    DOI: 10.1016/S0252-9602(07)60075-7

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GLOBAL EXISTENCE AND CONVERGENCE RATES OF SMOOTH SOLUTIONS FOR THE 3-D COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITHOUT HEAT CONDUCTIVITY GAO Zhen-Sheng, TAN Zhong, WU Guo-Chun Acta mathematica scientia,Series B    2014, 34 (1): 93-106.   DOI: 10.1016/S0252-9602(13)60129-0 Abstract （200）      PDF（pc） （195KB）（1254）       Save In this paper, we are concerned with the global existence and convergence rates of the smooth solutions for the compressible magnetohydrodynamic equations without heat conductivity, which is a hyperbolic-parabolic system. The global solutions are obtained by combining the local existence and a priori estimates if H3-norm of the initial perturbation around a constant states is small enough and its L1-norm is bounded. A priori decay-in-time estimates on the pressure, velocity and magnetic field are used to get the uniform bound of entropy. Moreover, the optimal convergence rates are also obtained. Reference | Related Articles | Metrics

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EXISTENCE AND STABILITY OF STANDING WAVES FOR A COUPLED NONLINEAR SCHR¨|ODINGER SYSTEM ZENG XiaoYu,ZHANG Yi Ming, ZHOU Huang Song Acta mathematica scientia,Series B    2015, 35 (1): 45-70.   DOI: 10.1016/S0252-9602(14)60138-7 Abstract （141）      PDF（pc） （294KB）（492）       Save We study the existence and stability of the standing waves of two coupled Schr¨odinger equations with potentials |x|bi (bi 2 R, i = 1, 2). Under suitable conditions on the growth of the nonlinear terms, we first establish the existence of standing waves of the Schr¨odinger system by solving a L2-normalized minimization problem, then prove that the set of all minimizers of this minimization problem is stable. Finally, we obtain the least energy solutions by the Nehari method and prove that the orbit sets of these least energy solutions are unstable, which generalizes the results of [11] where b1 = b2 = 2. Reference | Related Articles | Metrics

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CLASSIFICATION OF POSITIVE SOLUTIONS FOR NONLINEAR DIFFERENTIAL AND INTEGRAL SYSTEMS WITH CRITICAL EXPONENTS Wenxiong Chen, Congming Li Acta mathematica scientia,Series B    2009, 29 (4): 949-960.   DOI: 10.1016/S0252-9602(09)60079-5 Abstract （1098）      PDF（pc） （186KB）（2086）       Save We classify all positive solutions for the following integral system: ui(x) =∫Rn1/ |x − y|n−α fi(u(y))dy, x ∈ Rn, i = 1, · · · , m, 0 < α < n, and u(x) = (u1(x), u2(x), · · · , um(x)). Here fi(u), 1 ≤ i ≤ m, are real-valued functions of homogeneous degree n+α/ n−α and are monotone nondecreasing with respect to all the independent variables u1, u2, · · ·, um. In the special case n ≥ 3 and α = 2, we show that the above system is equivalent to the following elliptic PDE system: −△ui(x) = fi(u(x)), x ∈ Rn, i = 1, · · · , m, and u(x) = (u1(x), u2(x), · · · , um(x)). This system is closely related to the stationary Schr¨odinger system with critical exponents for Bose-Einstein condensate. Reference | Related Articles | Metrics

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A RISK-SENSITIVE STOCHASTIC MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL OF JUMP DIFFUSIONS AND ITS APPLICATIONS SHI Jing-Tao, WU Zhen Acta mathematica scientia,Series B    2011, 31 (2): 419-433.   DOI: 10.1016/S0252-9602(11)60242-7 Abstract （731）      PDF（pc） （204KB）（1883）       Save A stochastic maximum principle for the risk-sensitive optimal control problem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained. Reference | Related Articles | Metrics

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ATTRACTORS FOR FULLY DISCRETE FINITE DIFFERENCE SCHEME OF DISSIPATIVE ZAKHAROV EQUATIONS ZHANG Fa-Yong, GUO Bai-Ling Acta mathematica scientia,Series B    2012, 32 (6): 2431-2452.   DOI: 10.1016/S0252-9602(12)60190-8 Abstract （447）      PDF（pc） （255KB）（942）       Save A fully discrete finite difference scheme for dissipative Zakharov equations is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions, the stability of the difference scheme and the error bounds of optimal order of the difference solutions are obtained in L2 ×H1 ×H2 over a finite time interval (0, T]. Finally, the existence of a global attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme. Reference | Related Articles | Metrics

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A SHORT NOTE ABOUT EXPOSED POINTS IN REAL BANACH SPACES Antonio Aizpuru; Francisco J Garc Acta mathematica scientia,Series B    DOI: 10.1016/S0252-9602(08)60080-6

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RAZUMIKHIN-TYPE THEOREMS OF NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS Zhou Shaobo; Hu Shigeng Acta mathematica scientia,Series B    DOI: 10.1016/S0252-9602(09)60019-9

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INTERIOR ESTIMATES IN MORREY SPACES FOR SOLUTIONS OF ELLIPTIC EQUATIONS AND WEIGHTED BOUNDEDNESS FOR COMMUTATORS OF SINGULAR INTEGRAL OPERATORS LIU Lan-Zhe Acta mathematica scientia,Series B    2005, 25 (1): 89-94.   Abstract （812）      PDF（pc） （117KB）（2292）       Save It is proved that, for the nondivergence elliptic equations $\sum_{i,j=1}^n$  $a_{ij}u_{x_ix_j}=f$,  if $f$ belongs to the generalized Morrey spaces $L^{p,\varphi}(\omega)$, then $u_{x_ix_j}\in L^{p, \varphi}(\omega)$, where $u$ is the $W^{2,p}$-solution of the equations.  In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on $L^{p,\varphi}(\omega)$. \noindent\ke{\bf Key words}{\rm  Nondivergence elliptic equation, generalized Morrey space, commutator of singular integral operator, $A_p$ weight} Reference | Related Articles | Metrics

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CONVERGENCE RATE OF AN APPROXIMATION TO MULTIPLE INTEGRAL OF FBM HU Yao-Zhong, WANG Bao-Bin Acta mathematica scientia,Series B    2010, 30 (3): 975-992.   DOI: 10.1016/S0252-9602(10)60095-1 Abstract （864）      PDF（pc） （202KB）（1390）       Save In this article, we study the rate of convergence of the polygonal approximation to multiple stochastic integral Sp(f) of fractional Brownian motion of Hurst parameter H<1/2 when the fractional Brownian motion is replaced by its polygonal approximation. Under different conditions on f and for different p, we obtain different rates. Reference | Related Articles | Metrics

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MULTI-DIMENSIONAL GEOMETRIC BROWNIAN MOTIONS, ONSAGER-MACHLUP FUNCTIONS, AND APPLICATIONS TO MATHEMATICAL FINANCE 胡耀忠 Acta mathematica scientia,Series B    2000, 20 (3): 341-358.   Abstract （958）      PDF（pc） （185KB）（3905）       Save The solutions of the following bilinear stochastic differential equation are stud- ied dxt = Xm k=1 Ak t xtdwk(t) + Btxtdt where Ak t , Bt are (deterministic) continuous matrix-valued functions of t and w1(t), · · ·, wm(t) are m independent standard Brownian motions. Conditions are given such that the solution is positive if the initial condition is positive. The equation the most probable path must satisfy is also derived and applied to a mathematical finance problem. Reference | Related Articles | Metrics

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GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS FOR GENERALIZED POCHHAMMER-CHREE EQUATIONS XU Run-Zhang, LIU YA-Cheng Acta mathematica scientia,Series B    2010, 30 (5): 1793-1807.   DOI: 10.1016/S0252-9602(10)60173-7 Abstract （847）      PDF（pc） （200KB）（1357）       Save In this article, we study the initial boundary value problem of generalized Pochhammer-Chree equation utt-uxx-uxxt-uxxtt=f(u)xx, x ∈Ω, t >0, u(x, 0)=u0(x), ut(x, 0)=u1(x), x ∈Ω, u(0, t)=u(1, t)=0, t ≥0, where Ω =(0, 1). First, we obtain the existence of local Wk, p solutions. Then, we prove that, if f(s) ∈ in Ck+1(R) is ondecreasing, f(0)=0 and |f(u)| ≤ C1|u| ∫0uf(s)ds + C2, u0(x), u1(x) ∈Wk, p(Ω) ∩ W0{1, p}(Ω), k ≥1, 1< p ≤∞, then for any T>0 the problem admits a unique solution u(x, t) ∈ W2, ∞ (0, T; Wk, p(Ω)∩W01, p(Ω) ). Finally, the finite time blow-up of solutions and global Wk, p solution of generalized IMBq equations are discussed. Reference | Related Articles | Metrics

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ON THE REGULARITY CRITERIA OF THE 3D NAVIER-STOKES EQUATIONS IN CRITICAL SPACES DONG Bai-Qing, Sadek Gala, CHEN Zhi-Min Acta mathematica scientia,Series B    2011, 31 (2): 591-600.   DOI: 10.1016/S0252-9602(11)60259-2 Abstract （762）      PDF（pc） （173KB）（1572）       Save Regularity criteria of Leray-Hopf weak solutions to the three-dimensional  Navier-Stokes equations  in some critical spaces such as  Lorentz space, Morrey space and multiplier space are derived in terms of two partial derivatives, ∂1u1, ∂2u2, of  velocity fields. Reference | Related Articles | Metrics

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RAZUMIKHIN-TYPE THEOREM FOR NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY WU Fu-Ke, HU Shi-Geng, MAO Xue-Rong Acta mathematica scientia,Series B    2011, 31 (4): 1245-1258.   DOI: 10.1016/S0252-9602(11)60312-3 Abstract （731）      PDF（pc） （200KB）（1346）       Save This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with un-bounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations. Reference | Related Articles | Metrics

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THE RIEMANN PROBLEM WITH DELTA INITIAL DATA FOR THE ONE-DIMENSIONAL CHAPLYGIN GAS EQUATIONS WANG Zhen, ZHANG Qing-Ling Acta mathematica scientia,Series B    2012, 32 (3): 825-841.   DOI: 10.1016/S0252-9602(12)60064-2 Abstract （744）      PDF（pc） （285KB）（1364）       Save In this article, we study the Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations. Under the generalized Rankine-Hugoniot conditions and the entropy condition, we constructively obtain the global existence of generalized solutions that explicitly exhibit four kinds of different structures. Moreover, we obtain the stability of generalized solutions by making use of the perturbation of the initial data. Reference | Related Articles | Metrics