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25 June 2018, Volume 38 Issue 3 Previous Issue    Next Issue

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GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO THE HYPERBOLIC GEOMETRY FLOW WITH TIME-DEPENDENT DISSIPATION Dexing KONG, Qi LIU Acta mathematica scientia,Series B. 2018, 38 (3):  745-755.  DOI: 10.1016/S0252-9602(18)30780-X Abstract ( 93 )   RICH HTML PDF   Save In this article, we investigate the hyperbolic geometry flow with time-dependent dissipation (∂2gij)/(∂t2) + μ/((1 + t)λ) (∂gij)/∂t=-2Rij, on Riemann surface. On the basis of the energy method, for 0 < λ ≤ 1, μ > λ + 1, we show that there exists a global solution gij to the hyperbolic geometry flow with time-dependent dissipation with asymptotic flat initial Riemann surfaces. Moreover, we prove that the scalar curvature R(t, x) of the solution metric gij remains uniformly bounded. References | Related Articles | Metrics

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NONNEGATIVITY OF SOLUTIONS OF NONLINEAR FRACTIONAL DIFFERENTIAL-ALGEBRAIC EQUATIONS Xiaoli DING, Yaolin JIANG Acta mathematica scientia,Series B. 2018, 38 (3):  756-768.  DOI: 10.1016/S0252-9602(18)30781-1 Abstract ( 63 )   RICH HTML PDF   Save Nonlinear fractional differential-algebraic equations often arise in simulating integrated circuits with superconductors. How to obtain the nonnegative solutions of the equations is an important scientific problem. As far as we known, the nonnegativity of solutions of the nonlinear fractional differential-algebraic equations is still not studied. In this article, we investigate the nonnegativity of solutions of the equations. Firstly, we discuss the existence of nonnegative solutions of the equations, and then we show that the nonnegative solution can be approached by a monotone waveform relaxation sequence provided the initial iteration is chosen properly. The choice of initial iteration is critical and we give a method of finding it. Finally, we present an example to illustrate the efficiency of our method. References | Related Articles | Metrics

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GROWTH AND DISTORTION THEOREMS FOR ALMOST STARLIKE MAPPINGS OF COMPLEX ORDER λ Xiaofei ZHANG, Jin LU, Xiaofei LI Acta mathematica scientia,Series B. 2018, 38 (3):  769-777.  DOI: 10.1016/S0252-9602(18)30782-3 Abstract ( 101 )   RICH HTML PDF   Save In this article, the sharp growth theorem for almost starlike mappings of complex order λ is given firstly. Secondly, distortion theorem along a unit direction is also established as the application of the growth theorem. In particular, using our results can reduce to some well-known results. References | Related Articles | Metrics

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EXACT SOLUTIONS FOR THE CAUCHY PROBLEM TO THE 3D SPHERICALLY SYMMETRIC INCOMPRESSIBLE NAVIER-STOKES EQUATIONS Jianlin ZHANG, Yuming QIN Acta mathematica scientia,Series B. 2018, 38 (3):  778-790.  DOI: 10.1016/S0252-9602(18)30783-5 Abstract ( 77 )   RICH HTML PDF   Save In this article, we establish exact solutions to the Cauchy problem for the 3D spherically symmetric incompressible Navier-Stokes equations and further study the existence and asymptotic behavior of solution. References | Related Articles | Metrics

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PRODUCTS OF RESOLVENTS AND MULTIVALUED HYBRID MAPPINGS IN CAT(0) SPACES Gholamreza ZAMANI ESKANDANI, Soheila AZARMI, Masoumeh RAEISI Acta mathematica scientia,Series B. 2018, 38 (3):  791-804.  DOI: 10.1016/S0252-9602(18)30784-7 Abstract ( 91 )   RICH HTML PDF   Save In this article, we introduce and investigate the concept of multivalued hybrid mappings in CAT(0) spaces by using the concept of quasilinearization. Also, we present a new iterative algorithm involving products of Moreau-Yosida resolvents for finding a common element of the set of minimizers of a finite family of convex functions and a common fixed point of two multivalued hybrid mappings in CAT(0) spaces. References | Related Articles | Metrics

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CONVERGENCE FROM AN ELECTROMAGNETIC FLUID SYSTEM TO THE FULL COMPRESSIBLE MHD EQUATIONS Xin XU Acta mathematica scientia,Series B. 2018, 38 (3):  805-818.  DOI: 10.1016/S0252-9602(18)30785-9 Abstract ( 79 )   RICH HTML PDF   Save We are concerned with the zero dielectric constant limit for the full electromagneto-fluid dynamics in this article. This singular limit is justified rigorously for global smooth solution for both well-prepared and ill-prepared initial data. The explicit convergence rate is also obtained by a elaborate energy estimate. Moreover, we show that for the wellprepared initial data, there is no initial layer, and the electric field always converges strongly to the limit function. While for the ill-prepared data case, there will be an initial layer near t=0. The strong convergence results only hold outside the initial layer. References | Related Articles | Metrics

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ON ENTIRE SOLUTIONS OF SOME TYPE OF NONLINEAR DIFFERENCE EQUATIONS Huifang LIU, Zhiqiang MAO Acta mathematica scientia,Series B. 2018, 38 (3):  819-828.  DOI: 10.1016/S0252-9602(18)30786-0 Abstract ( 99 )   RICH HTML PDF   Save In this article, the existence of finite order entire solutions of nonlinear difference equations fn + Pd(z, f)=p1eα1z + p2eα2z are studied, where n ≥ 2 is an integer, Pd(z, f) is a difference polynomial in f of degree d(≤ n-2), p1, p2 are small meromorphic functions of ez, and α1, α2 are nonzero constants. Some necessary conditions are given to guarantee that the above equation has an entire solution of finite order. As its applications, we also find some type of nonlinear difference equations having no finite order entire solutions. References | Related Articles | Metrics

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CROSSED PRODUCTS BY FINITE GROUP ACTIONS WITH CERTAIN TRACIAL ROKHLIN PROPERTY Qingzhai Fan, Xiaochun Fang Acta mathematica scientia,Series B. 2018, 38 (3):  829-842.  DOI: 10.1016/S0252-9602(18)30787-2 Abstract ( 99 )   RICH HTML PDF   Save We introduce a special tracial Rokhlin property for unital C*-algebras. Let A be a unital tracial rank zero C*-algebra (or tracial rank no more than one C*-algebra). Suppose that α:G → Aut(A) is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C*-algebra. Then, the crossed product C*-algebra C*(G, A, α) has tracia rank zero (or has tracial rank no more than one). In fact, we get a more general results. References | Related Articles | Metrics

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BLOW-UP PROBLEMS FOR NONLINEAR PARABOLIC EQUATIONS ON LOCALLY FINITE GRAPHS Yong LIN, Yiting WU Acta mathematica scientia,Series B. 2018, 38 (3):  843-856.  DOI: 10.1016/S0252-9602(18)30788-4 Abstract ( 101 )   RICH HTML PDF   Save Let G=(V, E) be a locally finite connected weighted graph, and △ be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation ut=△u + f(u) on G. The blow-up phenomenons for ut=△u + f(u) are discussed in terms of two cases:(i) an initial condition is given; (ii) a Dirichlet boundary condition is given. We prove that if f satisfies appropriate conditions, then the corresponding solutions will blow up in a finite time. References | Related Articles | Metrics

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STABILITY OF RAREFACTION WAVE FOR A MACROSCOPIC MODEL DERIVED FROM THE VLASOV-MAXWELL-BOLTZMANN SYSTEM Yongting HUANG, Hongxia LIU Acta mathematica scientia,Series B. 2018, 38 (3):  857-888.  DOI: 10.1016/S0252-9602(18)30789-6 Abstract ( 65 )   RICH HTML PDF   Save In this article, we are concerned with the nonlinear stability of the rarefaction wave for a one-dimensional macroscopic model derived from the Vlasov-Maxwell-Boltzmann system. The result shows that the large-time behavior of the solutions coincides with the one for both the Navier-Stokes-Poisson system and the Navier-Stokes system. Both the timedecay property of the rarefaction wave profile and the influence of the electromagnetic field play a key role in the analysis. References | Related Articles | Metrics

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EXISTENCE OF GLOBAL L∞ SOLUTIONS TO A GENERALIZED n×n HYPERBOLIC SYSTEM OF LEROUX TYPE Shujun LIU, Fangqi CHEN, Zejun WANG Acta mathematica scientia,Series B. 2018, 38 (3):  889-897.  DOI: 10.1016/S0252-9602(18)30790-2 Abstract ( 57 )   RICH HTML PDF   Save In this article, we give the existence of global L∞ bounded entropy solutions to the Cauchy problem of a generalized n×n hyperbolic system of LeRoux type. The main difficulty lies in establishing some compactness estimates of the viscosity solutions because the system has been generalized from 2×2 to n×n and more linearly degenerate characteristic fields emerged, and the emergence of singularity in the region {v1=0} is another difficulty. We obtain the existence of the global weak solutions using the compensated compactness method coupled with the construction of entropy-entropy flux and BV estimates on viscous solutions. References | Related Articles | Metrics

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GLOBAL WELLPOSEDNESS OF MAGNETOHYDRODYNAMICS SYSTEM WITH TEMPERATURE-DEPENDENT VISCOSITY Shibin SU, Xiaokui ZHAO Acta mathematica scientia,Series B. 2018, 38 (3):  898-914.  DOI: 10.1016/S0252-9602(18)30791-4 Abstract ( 102 )   RICH HTML PDF   Save The initial boundary value problem of the one-dimensional magneto-hydrodynamics system, when the viscosity, thermal conductivity, and magnetic diffusion coefficients are general smooth functions of temperature, is considered in this article. A unique global classical solution is shown to exist uniquely and converge to the constant state as the time tends to infinity under certain assumptions on the initial data and the adiabatic exponent γ. The initial data can be large if γ is sufficiently close to 1. References | Related Articles | Metrics

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GLOBAL WEAK SOLUTIONS TO A GENERALIZED BENJAMIN-BONA-MAHONY-BURGERS EQUATION Rui LI, Chong LAI, Yonghong WU Acta mathematica scientia,Series B. 2018, 38 (3):  915-925.  DOI: 10.1016/S0252-9602(18)30792-6 Abstract ( 63 )   RICH HTML PDF   Save The existence of global weak solutions for a generalized Benjamin-Bona-MahonyBurgers equation is established in the space C([0, ∞)×R) ∩ L∞([0, ∞); H1(R)) under the condition that its initial value belongs to the space H1(R). A one-sided super bound estimate and a space-time higher-norm estimate on the first order derivatives of the solution with respect to the space variable are derived to prove the existence. References | Related Articles | Metrics

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A BOUNDARY SCHWARZ LEMMA FOR PLURIHARMONIC MAPPINGS FROM THE UNIT POLYDISK TO THE UNIT BALL Ling LI, Hongyi LI, Di ZHAO Acta mathematica scientia,Series B. 2018, 38 (3):  926-934.  DOI: 10.1016/S0252-9602(18)30793-8 Abstract ( 90 )   RICH HTML PDF   Save In this article, we present a Schwarz lemma at the boundary for pluriharmonic mappings from the unit polydisk to the unit ball, which generalizes classical Schwarz lemma for bounded harmonic functions to higher dimensions. It is proved that if the pluriharmonic mapping f ∈ P(Dn, BN) is C1+α at z0 ∈ Er ⊂ ∂Dn with f(0)=0 and f(z0)=w0 ∈ ∂BN for any n, N ≥ 1, then there exist a nonnegative vector λf=(λ1,0, …, λr, 0, …,0)T ∈ R2n satisfying λi ≥ 1/22n-1 for 1 ≤ i ≤ r such that (Df(z'0))T w'0=diag(λf)z'0, where z'0 and w'0 are real versions of z0 and w0, respectively. References | Related Articles | Metrics

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POSITIVE SOLUTIONS FOR A WEIGHTED FRACTIONAL SYSTEM Pengyan WANG, Yongzhong WANG Acta mathematica scientia,Series B. 2018, 38 (3):  935-949.  DOI: 10.1016/S0252-9602(18)30794-X Abstract ( 78 )   RICH HTML PDF   Save In this article, we study positive solutions to the system To reach our aim, by using the method of moving planes, we prove a narrow region principle and a decay at infinity by the iteration method. On the basis of these results, we conclude radial symmetry and monotonicity of positive solutions for the problems involving the weighted fractional system on an unit ball and the whole space. Furthermore, non-existence of nonnegative solutions on a half space is given. References | Related Articles | Metrics

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THE EVENTUALLY DISTANCE MINIMIZING RAYS IN MODULI SPACES Fei SONG, Yi QI, Guangming HU Acta mathematica scientia,Series B. 2018, 38 (3):  950-964.  DOI: 10.1016/S0252-9602(18)30795-1 Abstract ( 59 )   RICH HTML PDF   Save The eventually distance minimizing ray (EDM ray) in moduli spaces of the Riemann surfaces of analytic finite type with 3g +n-3 > 0 is studied, which was introduced by Farb and Masur[5]. The asymptotic distance of EDM rays in a moduli space and the distance of end points of EDM rays in the boundary of the moduli space in the augmented moduli space are discussed in this article. A relation between the asymptotic distance of EDM rays and the distance of their end points is established. It is proved also that the distance of end points of two EDM rays is equal to that of end points of two Strebel rays in the Teichmüller space of a covering Riemann surface which are leftings of some representatives of the EDM rays. Meanwhile, simpler proofs for some known results are given. References | Related Articles | Metrics

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A GENERALIZATION OF GAUSS-KUZMIN-LÉVY THEOREM Peng SUN Acta mathematica scientia,Series B. 2018, 38 (3):  965-972.  DOI: 10.1016/S0252-9602(18)30796-3 Abstract ( 74 )   RICH HTML PDF   Save We prove a generalized Gauss-Kuzmin-Lévy theorem for the generalized Gauss transformation Tp (x)={p/x}. In addition, we give an estimate for the constant that appears in the theorem. References | Related Articles | Metrics

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NONLINEAR STABILITY OF VISCOUS SHOCK WAVES FOR ONE-DIMENSIONAL NONISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH A CLASS OF LARGE INITIAL PERTURBATION Shaojun TANG, Lan ZHANG Acta mathematica scientia,Series B. 2018, 38 (3):  973-1000.  DOI: 10.1016/S0252-9602(18)30797-5 Abstract ( 97 )   RICH HTML PDF   Save We study the nonlinear stability of viscous shock waves for the Cauchy problem of one-dimensional nonisentropic compressible Navier-Stokes equations for a viscous and heat conducting ideal polytropic gas. The viscous shock waves are shown to be time asymptotically stable under large initial perturbation with no restriction on the range of the adiabatic exponent provided that the strengths of the viscous shock waves are assumed to be sufficiently small.The proofs are based on the nonlinear energy estimates and the crucial step is to obtain the positive lower and upper bounds of the density and the temperature which are uniformly in time and space. References | Related Articles | Metrics

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STABILITY OF TRAVELING WAVES IN A POPULATION DYNAMIC MODEL WITH DELAY AND QUIESCENT STAGE Yonghui ZHOU, Yunrui YANG, Kepan LIU Acta mathematica scientia,Series B. 2018, 38 (3):  1001-1024.  DOI: 10.1016/S0252-9602(18)30798-7 Abstract ( 68 )   RICH HTML PDF   Save This article is concerned with a population dynamic model with delay and quiescent stage. By using the weighted-energy method combining continuation method, the exponential stability of traveling waves of the model under non-quasi-monotonicity conditions is established. Particularly, the requirement for initial perturbation is weaker and it is uniformly bounded only at x=+∞ but may not be vanishing. References | Related Articles | Metrics

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LONG-TIME DYNAMICS OF THE STRONGLY DAMPED SEMILINEAR PLATE EQUATION IN RN Azer KHANMAMEDOV, Sema YAYLA Acta mathematica scientia,Series B. 2018, 38 (3):  1025-1042.  DOI: 10.1016/S0252-9602(18)30799-9 Abstract ( 85 )   RICH HTML PDF   Save We investigate the initial-value problem for the semilinear plate equation containing localized strong damping, localized weak damping and nonlocal nonlinearity. We prove that if nonnegative damping coefficients are strictly positive almost everywhere in the exterior of some ball and the sum of these coefficients is positive a.e. in Rn, then the semigroup generated by the considered problem possesses a global attractor in H2 (Rn)×L2 (Rn). We also establish the boundedness of this attractor in H3 (Rn)×H2 (Rn). References | Related Articles | Metrics

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INITIAL BOUNDARY VALUE PROBLEM FOR A NONCONSERVATIVE SYSTEM IN ELASTODYNAMICS K. Divya JOSEPH, P. A. DINESH Acta mathematica scientia,Series B. 2018, 38 (3):  1043-1056.  DOI: 10.1016/S0252-9602(18)30800-2 Abstract ( 47 )   RICH HTML PDF   Save This article is concerned with the initial boundary value problem for a nonconservative system of hyperbolic equation appearing in elastodynamics in the space time domain x > 0, t > 0. The number of boundary conditions, to be prescribed at the boundary x=0, depends on the number of characteristics entering the domain. Because our system is nonlinear, the characteristic speeds depends on the unknown and the direction of the characteristics curves are known apriori. As it is well known, the boundary condition has to be understood in a generalised way. One of the standard way is using vanishing viscosity method. We use this method to construct solution for a particular class of initial and boundary data, namely the initial and boundary datas that lie on the level sets of one of the Riemann invariants. References | Related Articles | Metrics

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HELICAL SYMMETRIC SOLUTION OF 3D NAVIER-STOKES EQUATIONS ARISING FROM GEOMETRIC SHAPE OF THE BOUNDARY Weifeng JIANG, Kaitai LI Acta mathematica scientia,Series B. 2018, 38 (3):  1057-1104.  DOI: 10.1016/S0252-9602(18)30801-4 Abstract ( 70 )   RICH HTML PDF   Save In this article, we investigate three-dimensional solution with helical symmetry in a gap between two concentric rotating cylinders, inside is a helicoidal surface (screw propeller) while outside is a cylindrical surface. Establish the partial differential equations and its variational formulation satisfied by a helical solution in a helical coordinate system using tensor analysis method, we provide a computational method for the power and propulsion of the screw. The existence and uniqueness of weak helical solutions are proved. References | Related Articles | Metrics