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GLOBAL EXISTENCE OF STRONG SOLUTIONS OF NAVIER-STOKES EQUATIONS WITH NON-NEWTONIAN POTENTIAL FOR ONE-DIMENSIONAL ISENTROPIC#br# COMPRESSIBLE FLUIDS YUAN Hong-Jun, LIU Hong-Zhi, QIAO Jie-Zeng, LI Fan-Pei Acta mathematica scientia,Series B    2012, 32 (4): 1467-1486.   DOI: 10.1016/S0252-9602(12)60116-7 Abstract （607）      PDF（pc） （208KB）（1220）       Save The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove two global existence results on strong solutions of isentropic compressible Navier-Stokes equations. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition. Reference | Related Articles | Metrics

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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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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 （1028）      PDF（pc） （222KB）（2391）       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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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）（2304）       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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THE INTERIOR LAYER PHENOMENA FOR A CLASS OF SINGULARLY PERTURBED DELAY-DIFFERENTIAL EQUATIONS WANG Na, NI Ming-Kang Acta mathematica scientia,Series B    2013, 33 (2): 532-542.   DOI: 10.1016/S0252-9602(13)60017-X Abstract （611）      PDF（pc） （172KB）（1074）       Save In this article, we study a kind of vector singularly perturbed delay-differential equation. Using boundary layer function method and geometric analysis skill, the asymptotic expression of the system is constructed and the uniform validity of asymptotic solution is also proved. Reference | Related Articles | Metrics

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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）（1262）       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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MATHEMATICAL ANALYSIS OF WEST NILE VIRUS MODEL WITH DISCRETE DELAYS Salisu M. GARBA, Mohammad A. SAFI Acta mathematica scientia,Series B    2013, 33 (5): 1439-1462.   DOI: 10.1016/S0252-9602(13)60095-8 Abstract （251）      PDF（pc） （467KB）（1363）       Save The paper presents the basic model for the transmission dynamics of West Nile virus (WNV). The model, which consists of seven mutually-exclusive compartments representing the birds and vector dynamics, has a locally-asymptotically stable disease-free equilibrium whenever the associated reproduction number (R0) is less than unity. As reveal in [3, 20], the analyses of the model show the existence of the phenomenon of backward bifurcation (where the stable disease-free equilibrium of the model co-exists with a stable endemic equilibrium when the reproduction number of the disease is less than unity). It is shown, that the backward bifurcation phenomenon can be removed by substituting the associated standard incidence function with a mass action incidence. Analysis of the reproduction number of the model shows that, the disease will persist, whenever R0 > 1, and increase in the length of incubation period can help reduce WNV burden in the community if a certain threshold quantities, denoted by Δb and Δv are  negative. On the other hand, increasing the length of the incubation period increases disease burden if Δb > 0 and Δv > 0. Furthermore, it is shown that adding time delay to the corresponding autonomous model with standard incidence (considered in [2]) does not alter the qualitative dynamics of the autonomous system (with respect to the elimination or persistence of the disease). Reference | Related Articles | Metrics

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PARAMETER ESTIMATION FOR A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY SMALL STABLE NOISES FROM DISCRETE OBSERVATIONS Long Hongwei Acta mathematica scientia,Series B    2010, 30 (3): 645-663.   DOI: 10.1016/S0252-9602(10)60067-7 Abstract （908）      PDF（pc） （217KB）（1405）       Save We study the least squares estimation of drift parameters for a class of stochastic differential equations driven by small α-stable noises, observed at n regularly spaced time points ti=i/n, i=1, …, n on [0,1]. Under some regularity conditions, we obtain the consistency and the rate of convergence of the least squares estimator(LSE) when a small dispersion parameter ε→0 and n → ∝simultaneously. The asymptotic distribution of the LSE in our setting is shown to be stable, which is completely different from the classical cases where asymptotic distributions are normal. Reference | Related Articles | Metrics

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INTERSECTION OF PRIME SUBMODULES AND DIMENSION OF MODULES A. Azizi Acta mathematica scientia,Series B    2005, 25 (3): 385-394.   Abstract （816）      PDF（pc） （178KB）（3803）       Save The aim of this paper is to study the conditions by which a P-prime sub- module can be expressed as a ¯nite intersection or union of P-prime submodules. Also corresponding to dimension and rank of modules, some equivalent conditions for a ring to be a Dedekind domain are given. Reference | Related Articles | Metrics

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GLOBAL WELL-POSEDNESS OF THE 2D INCOMPRESSIBLE MICROPOLAR FLUID FLOWS WITH PARTIAL VISCOSITY AND ANGULAR VISCOSITY CHEN Ming-Tao Acta mathematica scientia,Series B    2013, 33 (4): 929-935.   DOI: 10.1016/S0252-9602(13)60051-X Abstract （268）      PDF（pc） （139KB）（1213）       Save This paper is concerned with the two-dimensional equations of incompress-ible micropolar fluid flows with mixed partial viscosity and angular viscosity. The global existence and uniqueness of smooth solution to the Cauchy problem is established. Reference | Related Articles | Metrics

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TIME ASYMPTOTIC BEHAVIOR OF THE BIPOLAR NAVIER-STOKES-POISSON SYSTEM Hai-Liang Li, Tong Yang, Chen Zou Acta mathematica scientia,Series B    2009, 29 (6): 1721-1736.   DOI: 10.1016/S0252-9602(10)60013-6 Abstract （932）      PDF（pc） （214KB）（1621）       Save The bipolar Navier-Stokes-Poisson system (BNSP) has been used to simulate the transport of charged particles (ions and electrons for instance) under the influence of electrostatic force governed by the self-consistent Poisson equation. The optimal L2 time convergence rate for the global classical solution is obtained for a small initial perturbation of the constant equilibrium state. It is shown that due to the electric field, the difference of the charge densities tend to the equilibrium states at the optimal rate (1+t )-3/4 in L2-norm, while the individual momentum of the charged particles converges at the optimal rate (1+t )-1/4 which is slower than the rate (1+t )-3/4 for the compressible Navier-Stokes equations (NS). In addition, a new phenomenon on the charge transport is observed regarding the interplay between the two carriers that almost counteracts the influence of the electric field so that  the total density and  momentum of the two carriers converges at a faster rate (1+t )-3/4+ε for any small constant ε > 0. The above estimates reveal the essential difference between the unipolar and the bipolar Navier-Stokes-Poisson systems. Reference | Related Articles | Metrics

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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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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）（1354）       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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OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT FOR A CONSTANT ELASTICITY OF VARIANCE MODEL UNDER VARIANCE PRINCIPLE Jieming ZHOU, Yingchun DENG, Ya HUANG, Xiangqun YANG Acta mathematica scientia,Series B    2015, 35 (2): 303-312.   DOI: 10.1016/S0252-9602(15)60002-9 Abstract （91）      PDF（pc） （179KB）（1953）       Save This article studies the optimal proportional reinsurance and investment problem under a constant elasticity of variance (CEV) model. Assume that the insurer's surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer via the variance principle and invest in a risk-free asset and a risky asset whose price is modeled by a CEV model. The diffusion term can explain the uncertainty associated with the surplus of the insurer or the additional small claims. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. This optimization problem is studied in two cases depending on the diffusion term's explanation. In all cases, by using techniques of stochastic control theory, closed-form expressions for the value functions and optimal strategies are obtained. Reference | Related Articles | Metrics

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IMPROVED GAGLIARDO-NIRENBERG INEQUALITIES ON HEISENBERG TYPE GROUPS LUO Guang-Zhou Acta mathematica scientia,Series B    2011, 31 (4): 1583-1590.   DOI: 10.1016/S0252-9602(11)60344-5 Abstract （580）      PDF（pc） （164KB）（1439）       Save Motivated by the idea of M. Ledoux who brings out the connection between Sobolev embeddings and heat kernel bounds, we prove an analogous result for Kohn’s sub-Laplacian on the Heisenberg type groups. The main result includes features of an inequality of either Sobolev or Galiardo-Nirenberg type. Reference | Related Articles | Metrics

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SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m Harun Polat; Feyzi Basar Acta mathematica scientia,Series B    DOI: 10.1016/S0252-9602(07)60024-1

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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）（1398）       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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HÖLDER CONTINUOUS SOLUTIONS FOR SECOND ORDER INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES BU Shang-Quan Acta mathematica scientia,Series B    2011, 31 (3): 765-777.   DOI: 10.1016/S0252-9602(11)60274-9 Abstract （513）      PDF（pc） （200KB）（1274）       Save We study  H\"older continuous solutions for the second order integro-differential equations with infinite delay (P1): u''(t)+ cu'(t)+∫t-∞β (t-s)u'(s)ds+∫t-∞γ(t-s)u(s)ds =Au(t)-∫t-∞δ(t-s)Au(s)ds+f(t) on the line R, where 0 < α< 1, A is a closed operator in a complex Banach space X, c ∈C is a constant, f ∈Cα (R，X) and β, γ, δ ∈L1(R+). Under suitable assumptions on the kernels β, γ and δ, we completely characterize the Cα-well-posedness of (P1) by using operator-valued Cα-Fourier multipliers. Reference | Related Articles | Metrics

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ALL MEROMORPHIC SOLUTIONS OF AN AUXILIARY ORDINARY DIFFERENTIAL EQUATION AND ITS APPLICATIONS Wenjun YUAN, Weiling XIONG, Jianming LIN, Yonghong WU Acta mathematica scientia,Series B    2015, 35 (5): 1241-1250.   DOI: 10.1016/S0252-9602(15)30052-7 Abstract （78）      PDF（pc） （181KB）（1024）       Save In this paper, we first employ the complex method to deritive all meromorphic solutions of an auxiliary ordinary differential equation, and then find all meromorphic exact solutions of the modified ZK equation, modified KdV equation, nonlinear Klein-Gordon equation and modified BBM equation. Our work shows that there exist some classes of rational solutions wr,2(z) and simple periodic solutions ws,1(z) which are new and are not degenerated successively to by the elliptic function solutions. 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）（1132）       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