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25 August 2017, Volume 37 Issue 4 Previous Issue    Next Issue

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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 Abstract ( 107 )   RICH HTML PDF   Save 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 L1(Γ1), 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. References | Related Articles | Metrics

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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 Abstract ( 93 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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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 ( 116 )   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. References | Related Articles | Metrics

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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 Abstract ( 89 )   RICH HTML PDF   Save For 2 < γ < min{4, n}, we consider the focusing Hartree equation iut + △u + (|x|-γ *|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|-γ *|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]sc ≥ M[Q]1-scE[Q]sc and obtain a criteria on blow-up and global existence for the Hartree equation (0.1). References | Related Articles | Metrics

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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 Abstract ( 62 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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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 Abstract ( 75 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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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 Abstract ( 90 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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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 Abstract ( 102 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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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 ( 115 )   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]. References | Related Articles | Metrics

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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 Abstract ( 109 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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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 ( 118 )   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 u ∈ Lx,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). References | Related Articles | Metrics

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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 Abstract ( 109 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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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 Abstract ( 59 )   RICH HTML PDF   Save 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, n ∈ N+. 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. References | Related Articles | Metrics

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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 Abstract ( 65 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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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 Abstract ( 66 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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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 Abstract ( 86 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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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 Abstract ( 59 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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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 Abstract ( 83 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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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 Abstract ( 91 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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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 Abstract ( 73 )   RICH HTML PDF   Save We give a correction of Theorem 2.2 of Shen, Yin and Yan (2016). References | Related Articles | Metrics