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    25 August 2017, Volume 37 Issue 4 Previous Issue    Next Issue
    Articles
    RENORMALIZED SOLUTIONS OF ELLIPTIC EQUATIONS WITH ROBIN BOUNDARY CONDITIONS
    Olivier GUIBÉ, Alip OROPEZA
    Acta mathematica scientia,Series B. 2017, 37 (4):  889-910.  DOI: 10.1016/S0252-9602(17)30046-2
    In the present paper, we consider elliptic equations with nonlinear and nonhomogeneous Robin boundary conditions of the type

    where f and g are the element of L1(Ω) and L11), respectively. We define a notion of renormalized solution and we prove the existence of a solution. Under additional assumptions on the matrix field B we show that the renormalized solution is unique.
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    EXISTENCE OF SOLUTIONS OF NONLOCAL PERTURBATIONS OF DIRICHLET DISCRETE NONLINEAR PROBLEMS
    Alberto CABADA, Nikolay D. DIMITROV
    Acta mathematica scientia,Series B. 2017, 37 (4):  911-926.  DOI: 10.1016/S0252-9602(17)30047-4

    This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green's function to the linear part is done. The exact expression of the function is given, moreover the range of parameter for which it has constant sign is obtained. Using this, some existence results for the nonlinear problem are deduced from monotone iterative techniques, the classical Krasnoselski fixed point theorem or by application of recent fixed point theorems that combine both theories.

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    DYNAMICAL BEHAVIOR OF A STOCHASTIC HBV INFECTION MODEL WITH LOGISTIC HEPATOCYTE GROWTH
    Qun LIU, Daqing JIANG, Ningzhong SHI, Tasawar HAYAT, Ahmed ALSAEDI
    Acta mathematica scientia,Series B. 2017, 37 (4):  927-940.  DOI: 10.1016/S0252-9602(17)30048-6
    Abstract ( 106 )   RICH HTML PDF   Save

    This paper is concerned with a stochastic HBV infection model with logistic growth. First, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HBV infection model. Then we obtain sufficient conditions for extinction of the disease. The stationary distribution shows that the disease can become persistent in vivo.

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    GLOBAL WELL-POSEDNESS AND BLOW-UP FOR THE HARTREE EQUATION
    Lingyan YANG, Xiaoguang LI, Yonghong WU, Louis CACCETTA
    Acta mathematica scientia,Series B. 2017, 37 (4):  941-948.  DOI: 10.1016/S0252-9602(17)30049-8

    For 2 < γ < min{4, n}, we consider the focusing Hartree equation iut + △u + (|x| *|u|2)u=0, x ∈ Rn. (0.1) Let M[u] and E[u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of -△ Q + Q=(|x| *|Q|2)Q. Guo and Wang[Z. Angew. Math. Phy.,2014] established a dichotomy for scattering versus blow-up for the Cauchy problem of (0.1) if M[u]1-scE[u]sc < M[Q]1-scE[Q]sc(sc=γ-2/2). In this paper, we consider the complementary case M[u]1-scE[u]scM[Q]1-scE[Q]sc and obtain a criteria on blow-up and global existence for the Hartree equation (0.1).

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    ON THE GLOBAL EXISTENCE OF SMOOTH SOLUTIONS TO THE MULTI-DIMENSIONAL COMPRESSIBLE EULER EQUATIONS WITH TIME-DEPENDING DAMPING IN HALF SPACE
    Fei HOU
    Acta mathematica scientia,Series B. 2017, 37 (4):  949-964.  DOI: 10.1016/S0252-9602(17)30050-4

    This paper is a continue work of[4, 5]. In the previous two papers, we studied the Cauchy problem of the multi-dimensional compressible Euler equations with time-depending damping term -(μ/(1+t)λ)ρu, where λ ≥ 0 and μ > 0 are constants. We have showed that, for all λ ≥ 0 and μ > 0, the smooth solution to the Cauchy problem exists globally or blows up in finite time. In the present paper, instead of the Cauchy problem we consider the initialboundary value problem in the half space R+d with space dimension d=2, 3. With the help of the special structure of the equations and the fluid vorticity, we overcome the difficulty arisen from the boundary effect. We prove that there exists a global smooth solution for 0 ≤ λ < 1 when the initial data is close to its equilibrium state. In addition, exponential decay of the fluid vorticity will also be established.

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    STABILITY OF A VON KARMAN EQUATION WITH INFINITE MEMORY
    Sun-Hye PARK
    Acta mathematica scientia,Series B. 2017, 37 (4):  965-973.  DOI: 10.1016/S0252-9602(17)30051-6

    In this paper, we consider a von Karman equation with infinite memory. For von Karman equations with finite memory, there is a lot of literature concerning on existence of the solutions, decay of the energy, and existence of the attractors. However, there are few results on existence and energy decay rate of the solutions for von Karman equations with infinite memory. The main goal of the present paper is to generalize previous results by treating infinite history instead of finite history.

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    BLOW-UP AND LIFE SPAN ESTIMATES FOR A CLASS OF NONLINEAR DEGENERATE PARABOLIC SYSTEM WITH TIME-DEPENDENT COEFFICIENTS
    Anyin XIA, Mingshu FAN, Shan LI
    Acta mathematica scientia,Series B. 2017, 37 (4):  974-984.  DOI: 10.1016/S0252-9602(17)30052-8

    This paper deals with the singularity and global regularity for a class of nonlinear porous medium system with time-dependent coefficients under homogeneous Dirichlet boundary conditions. First, by comparison principle, some global regularity results are established. Secondly, using some differential inequality technique, we investigate the blow-up solution to the initial-boundary value problem. Furthermore, upper and lower bounds for the maximum blow-up time under some appropriate hypotheses are derived as long as blow-up occurs.

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    IMPULSIVE DIFFERENTIAL EQUATIONS WITH GAMMA DISTRIBUTED MOMENTS OF IMPULSES AND P-MOMENT EXPONENTIAL STABILITY
    R. AGARWAL, S. HRISTOVA, P. KOPANOV, D. O'REGAN
    Acta mathematica scientia,Series B. 2017, 37 (4):  985-997.  DOI: 10.1016/S0252-9602(17)30053-X

    Differential equations with impulses at random moments are set up and investigated. We study the case of Gamma distributed random moments of impulses. Several properties of solutions are studied based on properties of Gammma distributions. Some sufficient conditions for p-moment exponential stability of the solutions are given.

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    ORBITAL STABILITY OF PERIODIC TRAVELING WAVE SOLUTIONS TO THE GENERALIZED ZAKHAROV EQUATIONS
    Xiaoxiao ZHENG, Yadong SHANG, Xiaoming PENG
    Acta mathematica scientia,Series B. 2017, 37 (4):  998-1018.  DOI: 10.1016/S0252-9602(17)30054-1
    Abstract ( 112 )   RICH HTML PDF   Save
    This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations
    First, we prove the existence of a smooth curve of positive traveling wave solutions of dnoidal type with a fixed fundamental period L for the generalized Zakharov equations. Then, by using the classical method proposed by Benjamin, Bona et al., we show that this solution is orbitally stable by perturbations with period L. The results on the orbital stability of periodic traveling wave solutions for the generalized Zakharov equations in this paper can be regarded as a perfect extension of the results of[15, 16, 19].
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    CONDITIONAL EXPECTATIONS AND MARTINGALES IN NONCOMMUTATIVE Lp-SPACES ASSOCIATED WITH CENTER-VALUED TRACES
    Inomjon GANIEV, Farrukh MUKHAMEDOV
    Acta mathematica scientia,Series B. 2017, 37 (4):  1019-1032.  DOI: 10.1016/S0252-9602(17)30055-3

    In this paper we prove the existence of conditional expectations in the noncommutative Lp(M, Φ)-spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the obtained results, we establish the norm convergence of weighted averages of martingales in noncommutative Lp(M, Φ)-spaces.

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    LOCAL REGULARITY CRITERIA OF A SUITABLE WEAK SOLUTION TO MHD EQUATIONS
    Jae-Myoung KIM
    Acta mathematica scientia,Series B. 2017, 37 (4):  1033-1047.  DOI: 10.1016/S0252-9602(17)30056-5
    Abstract ( 105 )   RICH HTML PDF   Save

    We present a regularity condition of a suitable weak solution to the MHD equations in three dimensional space with slip boundary conditions for a velocity and magnetic vector fields. More precisely, we prove a suitable weak solution are Hölder continuous near boundary provided that the scaled mixed Lx,tp,q -norm of the velocity vector field with 3/p + 2/q ≤ 2, 2 < q < ∞ is sufficiently small near the boundary. Also, we will investigate that for this solution uLx,tp,q with 1 ≤ 3/p + 2/q ≤ 3/2, 3 < p < ∞, the Hausdorff dimension of its singular set is no greater than max{p,q}(3/p + 2/q -1).

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    ANALYSIS OF AN ELASTO-PIEZOELECTRIC SYSTEM OF HEMIVARIATIONAL INEQUALITIES WITH THERMAL EFFECTS
    Paweł SZAFRANIEC
    Acta mathematica scientia,Series B. 2017, 37 (4):  1048-1060.  DOI: 10.1016/S0252-9602(17)30057-7

    In this paper we prove the existence and uniqueness of a weak solution for a dynamic electo-viscoelastic problem that describes a contact between a body and a foundation. We assume the body is made from thermoviscoelastic material and consider nonmonotone boundary conditions for the contact.We use recent results from the theory of hemivariational inequalities and the fixed point theory.

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    SHARP WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE HIGHER-ORDER DISPERSIVE EQUATION
    Minjie JIANG, Wei YAN, Yimin ZHANG
    Acta mathematica scientia,Series B. 2017, 37 (4):  1061-1082.  DOI: 10.1016/S0252-9602(17)30058-9

    This current paper is devoted to the Cauchy problem for higher order dispersive equation
    ut + x2n+1u=x(u∂xnu) + xn-1(ux2), n ≥ 2, nN+.
    By using Besov-type spaces, we prove that the associated problem is locally well-posed in H(-n/2 + 3/4,-1/2n)(R). The new ingredient is that we establish some new dyadic bilinear estimates. When n is even, we also prove that the associated equation is ill-posed in H(s,a)(R) with s < -n/2 + 3/4 and all a ∈ R.

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    DUALITY OF WEIGHTED MULTIPARAMETER TRIEBEL-LIZORKIN SPACES
    Wei DING, Yueping ZHU
    Acta mathematica scientia,Series B. 2017, 37 (4):  1083-1104.  DOI: 10.1016/S0252-9602(17)30059-0

    In this paper, we reintroduce the weighted multi-parameter Triebel-Lizorkin spaces ?pα,q(ω; Rn1×Rn2) based on the Frazier and Jawerth' method in[11]. This space was firstly introduced in[18]. Then we establish its dual space and get that (?pα,q)*=CMOp-α,q' for 0 < p ≤ 1.

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    LEGENDRE SPECTRAL COLLOCATION METHOD FOR VOLTERRA-HAMMERSTEIN INTEGRAL EQUATION OF THE SECOND KIND
    Yunxia WEI, Yanping CHEN
    Acta mathematica scientia,Series B. 2017, 37 (4):  1105-1114.  DOI: 10.1016/S0252-9602(17)30060-7

    This paper is concerned with obtaining the approximate solution for VolterraHammerstein integral equation with a regular kernel. We choose the Gauss points associated with the Legendre weight function ω(x)=1 as the collocation points. The Legendre collocation discretization is proposed for Volterra-Hammerstein integral equation. We provide an error analysis which justifies that the errors of approximate solution decay exponentially in L2 norm and L norm. We give two numerical examples in order to illustrate the validity of the proposed Legendre spectral collocation method.

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    GEVREY REGULARITY WITH WEIGHT FOR INCOMPRESSIBLE EULER EQUATION IN THE HALF PLANE
    Feng CHENG, Wei-Xi LI, Chao-Jiang XU
    Acta mathematica scientia,Series B. 2017, 37 (4):  1115-1132.  DOI: 10.1016/S0252-9602(17)30061-9

    In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation for fast rotating fluid. The method presented here is based on the basic weighted L2-estimate, and the main difficulty arises from the estimate on the pressure term due to the appearance of weight function.

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    OPTIMALITY CONDITIONS AND DUALITY RESULTS FOR NONSMOOTH VECTOR OPTIMIZATION PROBLEMS WITH THE MULTIPLE INTERVAL-VALUED OBJECTIVE FUNCTION
    Tadeusz ANTCZAK
    Acta mathematica scientia,Series B. 2017, 37 (4):  1133-1150.  DOI: 10.1016/S0252-9602(17)30062-0

    In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a (weakly) LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a (weakly) LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple intervalobjective function are convex.

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    MÖBIUS-TODA HIERARCHY AND ITS INTEGRABILITY
    Chuanzhong LI
    Acta mathematica scientia,Series B. 2017, 37 (4):  1151-1161.  DOI: 10.1016/S0252-9602(17)30063-2

    In this paper, we construct a new integrable equation called Möbius-Toda equation which is a generalization of q-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of the Möbius-Toda equation and a whole integrable Möbius-Toda hierarchy are also constructed. To show the integrability, the bi-Hamiltonian structure and tau symmetry of the Möbius-Toda hierarchy are given and this leads to the existence of the tau function.

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    ON THE FIRST EIGENVALUE OF THE MEAN FINSLER-LAPLACIAN
    Qun HE, Fanqi ZENG, Daxiao ZENG
    Acta mathematica scientia,Series B. 2017, 37 (4):  1162-1172.  DOI: 10.1016/S0252-9602(17)30064-4

    In this paper, we prove that several different definitions of the Finsler-Laplacian are equivalent. Then we prove that any Berwald metric is affinely equivalent to its mean metric and give some upper or lower bound estimates for the first eigenvalue of the mean Laplacian on Berwald manifolds, which generalize some results in Riemannian geometry.

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    ERRATUM TO:LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION
    Guangjun SHEN, Xiuwei YIN, Litan YAN
    Acta mathematica scientia,Series B. 2017, 37 (4):  1173-1176.  DOI: 10.1016/S0252-9602(17)30065-6

    We give a correction of Theorem 2.2 of Shen, Yin and Yan (2016).

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