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25 October 2016, Volume 36 Issue 5 Previous Issue    Next Issue

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WELL-POSEDNESS OF A NONLINEAR MODEL OF PROLIFERATING CELL POPULATIONS WITH INHERITED CYCLE LENGTH Abdul-Majeed AL-IZERI, Khalid LATRACH Acta mathematica scientia,Series B. 2016, 36 (5):  1225-1244.  DOI: 10.1016/S0252-9602(16)30066-2 Abstract ( 68 )   RICH HTML PDF   Save This paper deals with a nonlinear initial boundary values problem derived from a modified version of the so called Lebowitz and Rubinow's model[16] discussed in[8, 9] modeling a proliferating age structured cell population with inherited properties. We give existence and uniqueness results on appropriate weighted Lp-spaces with 1≤p<∞ in the case where the rate of cells mortality σ and the transition rate k are depending on the total density of population. General local and nonlocal reproduction rules are considered. References | Related Articles | Metrics

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THE WEINSTEIN CONJECTURE IN PRODUCT OF SYMPLECTIC MANIFOLDS Yanqiao DING, Jianxun HU Acta mathematica scientia,Series B. 2016, 36 (5):  1245-1261.  DOI: 10.1016/S0252-9602(16)30067-4 Abstract ( 70 )   RICH HTML PDF   Save In this paper, using pseudo-holomorphic curve method, one proves the Weinstein conjecture in the product P1×P2 of two strongly geometrically bounded symplectic manifolds under some conditions with P1. In particular, if N is a closed manifold or a noncompact manifold of finite topological type, our result implies that the Weinstein conjecture in CP2×T*N holds. References | Related Articles | Metrics

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EXISTENCE AND UNIQUENESS OF ENTROPY SOLUTION TO PRESSURELESS EULER SYSTEM WITH A FLOCKING DISSIPATION Chunyin JIN Acta mathematica scientia,Series B. 2016, 36 (5):  1262-1284.  DOI: S0252-9602(16)30068-6 Abstract ( 47 )   RICH HTML PDF   Save We study the existence and uniqueness problem for the nonhomogeneous pressureless Euler system with the initial density being a Radon measure. Our uniqueness result is obtained in the same space as the existence theorem. Besides, by counterexample we prove that Huang-Wang's energy condition is also necessary for our nonhomogeneous system. References | Related Articles | Metrics

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SOLVABILITY OF A PARABOLIC-HYPERBOLIC TYPE CHEMOTAXIS SYSTEM IN 1-DIMENSIONAL DOMAIN Hua CHEN, Wenbin LÜ, Shaohua WU Acta mathematica scientia,Series B. 2016, 36 (5):  1285-1304.  DOI: S0252-9602(16)30069-8 Abstract ( 47 )   RICH HTML PDF   Save In this paper, we use contraction mapping principle, operator-theoretic approach and some uniform estimates to establish local solvability of the parabolic-hyperbolic type chemotaxis system with fixed boundary in 1-dimensional domain. In addition, local solvability of the free boundary problem is considered by straightening the free boundary. References | Related Articles | Metrics

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EXISTENCE AND NONEXISTENCE OF SOLUTIONS FOR A HARMONIC EQUATION WITH CRITICAL NONLINEARITY Kamal OULD BOUH Acta mathematica scientia,Series B. 2016, 36 (5):  1305-1316.  DOI: 10.1016/S0252-9602(16)30070-4 Abstract ( 60 )   RICH HTML PDF   Save This paper is concerned with the harmonic equation (P?ε):△u=0, u>0 in Bn and (∂u)/(∂ν)+(n-2)/(2)u=(n-2)/(2)Ku(n)/(n-2)?ε on Sn-1 where Bn is the unit ball in Rn, n≥4 with Euclidean metric g0, ∂Bn=Sn-1 is its boundary, K is a function on Sn-1 and ε is a small positive parameter. We construct solutions of the subcritical equation (P-ε) which blow up at one critical point of K. We give also a sufficient condition on the function K to ensure the nonexistence of solutions for (P-ε) which blow up at one point. Finally, we prove a nonexistence result of single peaked solutions for the supercritical equation (P+ε). References | Related Articles | Metrics

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FRACTIONAL INTEGRAL INEQUALITIES AND THEIR APPLICATIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS Yaghoub JALILIAN Acta mathematica scientia,Series B. 2016, 36 (5):  1317-1330.  DOI: 10.1016/S0252-9602(16)30071-6 Abstract ( 86 )   RICH HTML PDF   Save In this paper, first we obtain some new fractional integral inequalities. Then using these inequalities and fixed point theorems, we prove the existence of solutions for two different classes of functional fractional differential equations. References | Related Articles | Metrics

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LIMITING DIRECTION AND BAKER WANDERING DOMAIN OF ENTIRE SOLUTIONS OF DIFFERENTIAL EQUATIONS Jun WANG, Zongxuan CHEN Acta mathematica scientia,Series B. 2016, 36 (5):  1331-1342.  DOI: 10.1016/S0252-9602(16)30072-8 Abstract ( 53 )   RICH HTML PDF   Save In this paper, we mainly investigate entire solutions of complex differential equations with coefficients involving exponential functions, and obtain the dynamical properties of the solutions, their derivatives and primitives. With some conditions on coefficients, for the solutions, their derivatives and their primitives, we consider the common limiting directions of Julia set and the existence of Baker wandering domain. References | Related Articles | Metrics

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LEVEL SETS AND EQUIVALENCES OF MORAN-TYPE SETS Yali DU, Junjie MIAO, Min WU Acta mathematica scientia,Series B. 2016, 36 (5):  1343-1357.  DOI: 10.1016/S0252-9602(16)30073-X Abstract ( 78 )   RICH HTML PDF   Save In the paper, we consider Moran-type sets Ea given by sequences {akand {nk. we prove that Ea may be decompose into the disjoint union of level sets. Moreover, we define three type of equivalence between two dimension functions associated to two Morantype sets, respectively, and we classify Moran-type sets by these equivalent relations. References | Related Articles | Metrics

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THE HOLOMORPHIC AUTOMORPHISM GROUP OF HIGHER DIMENSION THULLEN DOMAIN Hongjun LI, Chunhui QIU Acta mathematica scientia,Series B. 2016, 36 (5):  1358-1368.  DOI: 10.1016/S0252-9602(16)30074-1 Abstract ( 61 )   RICH HTML PDF   Save In this paper, we give the holomorphic automorphism group of the higherdimensional generalization of Thullen domain. References | Related Articles | Metrics

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TIME DECAY RATE OF SOLUTIONS TO THE HYPERBOLIC MHD EQUATIONS IN R3 Bei LI, Hongjin ZHU, Caidi ZHAO Acta mathematica scientia,Series B. 2016, 36 (5):  1369-1382.  DOI: 10.1016/S0252-9602(16)30075-3 Abstract ( 68 )   RICH HTML PDF   Save In this paper, we first show the global existence, uniqueness and regularity of weak solutions for the hyperbolic magnetohydrodynamics (MHD) equations in R3. Then we establish that the solutions with initial data belonging to Hm(R3)∩L1(R3) have the following time decay rate:‖▽mu(x, t)‖2+‖▽mb(x, t)‖2+‖▽m+1u(x, t)‖2+‖▽m+1b(x, t)‖2≤c(1+t)-3/2-m for large t, where m=0, 1. References | Related Articles | Metrics

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STRONGLY NONLINEAR VARIATIONAL PARABOLIC EQUATIONS WITH p(x)-GROWTH Elhoussine AZROUL, Badr LAHMI, Ahmed YOUSSFI Acta mathematica scientia,Series B. 2016, 36 (5):  1383-1404.  DOI: 10.1016/S0252-9602(16)30076-5 Abstract ( 89 )   RICH HTML PDF   Save We study the Dirichlet problem associated to strongly nonlinear parabolic equations involving p(x) structure in W01,xLp(x)(Q). We prove the existence of weak solutions by applying Galerkin's approximation method. References | Related Articles | Metrics

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UNIFORM FORMULA FOR THE RIEMANN SOLUTIONS OF A SCALAR COMBUSTION MODEL Chunlong YANG, Gaowei CAO, Xiaozhou YANG Acta mathematica scientia,Series B. 2016, 36 (5):  1405-1418.  DOI: 10.1016/S0252-9602(16)30077-7 Abstract ( 66 )   RICH HTML PDF   Save In this paper, we construct a uniform formula for the Riemann solutions of the simplified Chapman-Jouguet model. Firstly, we define a new functional, and then, we obtain that the Riemann solutions can be expressed by the maximum value point of this functional, while Riemann solutions may contain some of strong detonation waves, Chapman-Jouguet detonation waves and contact discontinuities. Finally, Chapman-Jouguet deflagration waves are also discussed. References | Related Articles | Metrics

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GLOBAL CLASSICAL SOLUTION TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY Yulin YE Acta mathematica scientia,Series B. 2016, 36 (5):  1419-1432.  DOI: 10.1016/S0252-9602(16)30078-9 Abstract ( 83 )   RICH HTML PDF   Save In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ) provided that the initial energy is small in some sense. In our result, we give a relation between the initial energy and the viscosity coefficient μ, and it shows that the initial energy can be large if the coefficient of the viscosity μ is taken to be large, which implies that large viscosity μ means large solution. References | Related Articles | Metrics

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STRONG CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEM AND BREGMAN TOTALLY QUASI-ASYMPTOTICALLY NONEXPANSIVE MAPPING IN BANACH SPACES Sheng ZHU, Jianhua HUANG Acta mathematica scientia,Series B. 2016, 36 (5):  1433-1444.  DOI: 10.1016/S0252-9602(16)30079-0 Abstract ( 54 )   RICH HTML PDF   Save In this paper, we propose a new hybrid iterative scheme for finding a common solution of an equilibrium problem and fixed point of Bregman totally quasi-asymptotically nonexpansive mapping in reflexive Banach spaces. Moreover, we prove some strong convergence theorems under suitable control conditions. Finally, the application to zero point problem of maximal monotone operators is given by the result. References | Related Articles | Metrics

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GENERALIZED WARDOWSKI TYPE FIXED POINT THEOREMS VIA α-ADMISSIBLE FG-CONTRACTIONS IN b-METRIC SPACES Vahid PARVANEH, Nawab HUSSAIN, Zoran KADELBURG Acta mathematica scientia,Series B. 2016, 36 (5):  1445-1456.  DOI: 10.1016/S0252-9602(16)30080-7 Abstract ( 62 )   RICH HTML PDF   Save Recently, Wardowski [Fixed Point Theory Appl., 2012:94, 2012] introduced and studied a new contraction called F-contraction to prove a fixed point result as a generalization of the Banach contraction principle. In this paper, we introduce an α-β-FG-contraction and generalize the Wardowski fixed point result in b-metric and ordered b-metric spaces. As an application of our results we deduce Suzuki type fixed point results for β-FG-contractions. Moreover, we discuss some illustrative examples to highlight the realized improvements. References | Related Articles | Metrics

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ASYMPTOTIC SOLUTION OF SINGULARLY PERTURBED HYBRID DYNAMICAL SYSTEMS Limeng WU, Juan ZHANG, Mingkang NI, Haibo LU Acta mathematica scientia,Series B. 2016, 36 (5):  1457-1466.  DOI: 10.1016/S0252-9602(16)30081-9 Abstract ( 50 )   RICH HTML PDF   Save In this paper, we consider a class of optimal control problem for the singularly perturbed hybrid dynamical systems. By means of variational method, we obtain the necessary conditions of the hybrid dynamical systems. Meanwhile, the existence of solution for the hybrid dynamical system is proved by the sewing method and the uniformly valid asymptotic expansion of the optimal trajectory is constructed by the boundary function method. Finally, an example is presented to illustrate the result. References | Related Articles | Metrics

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WANDERING SUBSPACES OF THE HARDY-SOBOLEV SPACES OVER Dn Jiesheng XIAO, Guangfu CAO Acta mathematica scientia,Series B. 2016, 36 (5):  1467-1473.  DOI: 10.1016/S0252-9602(16)30082-0 Abstract ( 59 )   RICH HTML PDF   Save In this paper, we show that for (log(2)/(3))/(2 log 2)≤β≤(1)/(2), suppose S is an invariant subspace of the Hardy-Sobolev spaces Hβ2(Dn) for the n-tuple of multiplication operators (Mz1,…, Mzn). If (Mz1|S,…, Mzn|S) is doubly commuting, then for any non-empty subset α={α1,…, αk} of {1,…,n}, WαS is a generating wandering subspace for Wα|S=(Mzα1|S,…, Mzαk|S), that is,[WαS]Wα|S=S, where WαS(S?zαiS). References | Related Articles | Metrics

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VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS Jing ZHAO, Shengnan WANG Acta mathematica scientia,Series B. 2016, 36 (5):  1474-1486.  DOI: 10.1016/S0252-9602(16)30083-2 Abstract ( 110 )   RICH HTML PDF   Save Let H1, H2, H3 be real Hilbert spaces, let A:H1→H3, B:H2→H3 be two bounded linear operators. The split equality common fixed point problem (SECFP) in the infinite-dimensional Hilbert spaces introduced by Moudafi (Alternating CQ-algorithm for convex feasibility and split fixed-point problems. Journal of Nonlinear and Convex Analysis) is to find x∈F(U), y∈F(T) such that Ax=By, (1) where U:H1→H1 and T:H2→H2 are two nonlinear operators with nonempty fixed point sets F(U)={x∈H1:Ux=x} and F(T)={x∈H2:Tx=x}. Note that, by taking B=I and H2=H3 in (1), we recover the split fixed point problem originally introduced in Censor and Segal. Recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms with weak convergence for the SECFP (1) of firmly quasi-nonexpansive operators. In this paper, we introduce two viscosity iterative algorithms for the SECFP (1) governed by the general class of quasi-nonexpansive operators. We prove the strong convergence of algorithms. Our results improve and extend previously discussed related problems and algorithms. References | Related Articles | Metrics

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RIESZ IDEMPOTENT OF (n,k)-QUASI-*-PARANORMAL OPERATORS Qingping ZENG, Huaijie ZHONG Acta mathematica scientia,Series B. 2016, 36 (5):  1487-1491.  DOI: 10.1016/S0252-9602(16)30084-4 Abstract ( 104 )   RICH HTML PDF   Save A bounded linear operator T on a complex Hilbert space H is called (n, k)-quasi-*-paranormal if ‖T1+n(Tkx)‖1/(1+n)‖Tkx‖1/(1+n)≥‖T*(Tkx)‖ for all x∈H, where n, k are nonnegative integers. This class of operators has many interesting properties and contains the classes of n-*-paranormal operators and quasi-*-paranormal operators. The aim of this note is to show that every Riesz idempotent Eλ with respect to a non-zero isolated spectral point λ of an (n)-quasi-*-paranormal operator T is self-adjoint and satisfies ranEλ=ker(T-λ)=ker(T-λ)*. References | Related Articles | Metrics

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PIECEWISE CONTINUOUS SOLUTIONS OF INITIAL VALUE PROBLEMS OF SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS Yuji LIU Acta mathematica scientia,Series B. 2016, 36 (5):  1492-1508.  DOI: 10.1016/S0252-9602(16)30085-6 Abstract ( 93 )   RICH HTML PDF   Save Results on the existence of piecewise continuous solutions for two classes of initial value problems of impulsive singular fractional differential equations are obtained. References | Related Articles | Metrics

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EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY Sanjukta DAS, Dwijendra PANDEY, N. SUKAVANAM Acta mathematica scientia,Series B. 2016, 36 (5):  1509-1523.  DOI: 10.1016/S0252-9602(16)30086-8 Abstract ( 145 )   RICH HTML PDF   Save This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained by use of measure of non-compactness. In the second section the conditions for approximate controllability are investigated for the distributed second order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. Our method is an extension of co-author N. Sukavanam's novel approach in[22]. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in[5], which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in[20], which are practically difficult to verify and apply. An example is provided to illustrate the presented theory. References | Related Articles | Metrics

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COEXISTENCE FOR MULTIPLE LARGEST REPRODUCTION RATIOS OF A MULTI-STRAIN SIS EPIDEMIC MODEL Yoshiaki MUROYA, Eleonora MESSINA, Elvira RUSSO, Antonia VECCHIO Acta mathematica scientia,Series B. 2016, 36 (5):  1524-1530.  DOI: 10.1016/S0252-9602(16)30087-X Abstract ( 70 )   RICH HTML PDF   Save In this paper, to complete the global dynamics of a multi-strains SIS epidemic model, we establish a precise result on coexistence for the cases of the partial and complete duplicated multiple largest reproduction ratios for this model. References | Related Articles | Metrics

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A SPECIAL MODULUS OF CONTINUITY AND THE K-FUNCTIONAL Nadezhda DOLMATOVA Acta mathematica scientia,Series B. 2016, 36 (5):  1531-1540.  DOI: 10.1016/S0252-9602(16)30088-1 Abstract ( 56 )   RICH HTML PDF   Save We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre's K-functional. We also prove Jackson's inequality for the approximation by trigonometric polynomials. References | Related Articles | Metrics