Acta Mathematica Scientia (Series B)
Sponsored by Wuhan Institute of Physics and
           Mathematics, CAS, China
Edited by  Editorial Committee of Acta Mathematica
           Scientia
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ISSN 0252-9602
CN  42-1227/O
25 December 2019, Volume 39 Issue 6 Previous Issue   
DECAY ESTIMATE AND GLOBAL EXISTENCE OF SEMILINEAR THERMOELASTIC TIMOSHENKO SYSTEM WITH TWO DAMPING EFFECTS
Weike WANG, Rui XUE
Acta mathematica scientia,Series B. 2019, 39 (6):  1461-1486.  DOI: 10.1007/s10473-019-0601-z
Abstract ( 29 )   RICH HTML PDF(550KB) ( 41 )   Save
In this paper, we study a semilinear Timoshenko system with heat conduction having two damping effects. The observation that two damping effects might lead to smaller decay rates for solutions in comparison to one damping effect is rigorously proved here in providing optimality results. Moreover, the global well-posedness for small data is presented.
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SHUBIN REGULARITY FOR THE RADIALLY SYMMETRIC SPATIALLY HOMOGENEOUS BOLTZMANN EQUATION WITH DEBYE-YUKAWA POTENTIAL
Léo GLANGETAS, Haoguang LI
Acta mathematica scientia,Series B. 2019, 39 (6):  1487-1507.  DOI: 10.1007/s10473-019-0602-y
Abstract ( 12 )   RICH HTML PDF(477KB) ( 15 )   Save
In this work, we study the Cauchy problem for the radially symmetric spatially homogeneous Boltzmann equation with Debye-Yukawa potential. We prove that this Cauchy problem enjoys the same smoothing effect as the Cauchy problem defined by the evolution equation associated to a fractional logarithmic harmonic oscillator. To be specific, we can prove the solution of the Cauchy problem belongs to Shubin spaces.
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SYMMETRY OF POSITIVE SOLUTIONS FOR THE FRACTIONAL HARTREE EQUATION
Xiangqing Liu
Acta mathematica scientia,Series B. 2019, 39 (6):  1508-1516.  DOI: 10.1007/s10473-019-0603-x
Abstract ( 13 )   RICH HTML PDF(248KB) ( 14 )   Save
In this paper, by using the method of moving planes, we are concerned with the symmetry and monotonicity of positive solutions for the fractional Hartree equation.
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ON THE STABILITY OF A THERMOELASTIC LAMINATED BEAM
Tijani A. APALARA
Acta mathematica scientia,Series B. 2019, 39 (6):  1517-1524.  DOI: 10.1007/s10473-019-0604-9
Abstract ( 9 )   RICH HTML PDF(224KB) ( 9 )   Save
In this paper we consider a one-dimensional laminated beam system. The only dissipation in the system is through heat conduction in the interfacial slip equation. We prove that this unique dissipation is strong enough to exponentially stabilize the system provided the wave speeds of the system are equal. This result extends previous works where additional internal or boundary controls were used together with a frictional damping in the interfacial slip.
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GLOBAL EXISTENCE AND DECAY ESTIMATES FOR THE CLASSICAL SOLUTIONS TO A COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL
Shijin DING, Bingyuan HUANG, Quanrong LI
Acta mathematica scientia,Series B. 2019, 39 (6):  1525-1537.  DOI: 10.1007/s10473-019-0605-8
Abstract ( 13 )   RICH HTML PDF(338KB) ( 12 )   Save
We prove the global existence of classical solutions to a fluid-particle interaction model in R3, namely, compressible Navier-Stokes-Smoluchowski equations, when the initial data are close to the stationary state (ρ, 0, η) and the external potential satisfies the smallness assumption. Furthermore, optimal decay rates of classical solutions in H3-framework are obtained.
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GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR SOME COUPLED SYSTEMS VIA A LYAPUNOV FUNCTIONAL
Lamia DJEBARA, Salem ABDELMALEK, Samir BENDOUKHA
Acta mathematica scientia,Series B. 2019, 39 (6):  1538-1550.  DOI: 10.1007/s10473-019-0606-7
Abstract ( 5 )   RICH HTML PDF(760KB) ( 4 )   Save
The purpose of this work is to study the global existence and asymptotic behavior of solutions to a coupled reaction-diffusion system describing epidemiological or chemical situations. Our analytical proofs are based on the Lyapunov functional methods.
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WELL-POSEDNESS AND STABILITY FOR THE GENERALIZED INCOMPRESSIBLE MAGNETO-HYDRODYNAMIC EQUATIONS IN CRITICAL FOURIER-BESOV-MORREY SPACES
Azzeddine EL BARAKA, Mohamed TOUMLILIN
Acta mathematica scientia,Series B. 2019, 39 (6):  1551-1567.  DOI: 10.1007/s10473-019-0607-6
Abstract ( 2 )   RICH HTML PDF(416KB) ( 1 )   Save
This paper concerns the Cauchy problem of the 3D generalized incompressible magneto-hydrodynamic (GMHD) equations. By using the Fourier localization argument and the Littlewood-Paley theory, we get local well-posedness results of the GMHD equations with large initial data (u0, b0) belonging to the critical Fourier-Besov-Morrey spaces FṄp,λ,q1-2α+ 3/p'+λ/p (R3). Moreover, stability of global solutions is also discussed.
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ON THE EXISTENCE AND STABILITY OF BOUNDARY VALUE PROBLEM FOR DIFFERENTIAL EQUATION WITH HILFER-KATUGAMPOLA FRACTIONAL DERIVATIVE
E. M. ELSAYED, S. HARIKRISHNAN, K. KANAGARAJAN
Acta mathematica scientia,Series B. 2019, 39 (6):  1568-1578.  DOI: 10.1007/s10473-019-0608-5
Abstract ( 4 )   RICH HTML PDF(286KB) ( 5 )   Save
In this paper, we discuss the existence, uniqueness and stability of boundary value problem for differential equation with Hilfer-Katugampola fractional derivative. The arguments are based upon Schaefer's fixed point theorem, Banach contraction principle and Ulam type stability.
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NEW RESULTS FOR A CLASS OF UNIVALENT FUNCTIONS
Zhigang PENG, Milutin OBRADOVI?
Acta mathematica scientia,Series B. 2019, 39 (6):  1579-1588.  DOI: 10.1007/s10473-019-0609-4
Abstract ( 10 )   RICH HTML PDF(274KB) ( 10 )   Save
Let A denote the family of all analytic functions f(z) in the unit disk D={z ∈ C:|z|<1}, normalized by the conditions f(0)=0 and f'(0)=1. Let U denote the set of all functions fA satisfying the condition
|(z/f(z))2 f'(z) -1|<1 for zD.
Let Ω be the class of all fA for which
|zf'(z) -f(z)|<1/2, z ∈ D.
In this paper, the relations between the two classes are discussed. Furthermore, some new results on the class Ω are obtained.
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STABILITY OF MONOSTABLE WAVES FOR A NONLOCAL EQUATION WITH DELAY AND WITHOUT QUASI-MONOTONICITY
Kepan LIU, Yunrui Yang, Yang YANG
Acta mathematica scientia,Series B. 2019, 39 (6):  1589-1604.  DOI: 10.1007/s10473-019-0610-y
Abstract ( 8 )   RICH HTML PDF(384KB) ( 7 )   Save
By using the weighted-energy method combining continuation method, the exponential stability of monostable traveling waves for a delayed equation without quasi-monotonicity is established, including even the slower waves whose speed are close to the critical speed. Particularly, the nonlinearity is nonlocal in the equation and the initial perturbation is uniformly bounded only at x=+∞ but may not be vanishing.
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FRACTIONAL HALANAY INEQUALITY AND APPLICATION IN NEURAL NETWORK THEORY
Nasser-eddine TATAR
Acta mathematica scientia,Series B. 2019, 39 (6):  1605-1618.  DOI: 10.1007/s10473-019-0611-x
Abstract ( 2 )   RICH HTML PDF(334KB) ( 3 )   Save
The (integer order) Halanay inequality with distributed delays is extended to the fractional order case. It is proved that solutions decay to zero as a Mittag-Leffler function as time goes to infinity provided that the delay feedback are bounded by similar functions. An application to a problem arising in neural network theory is provided showing that the equilibrium is Mittag-Leffler stable.
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CONVEX MAPPINGS ASSOCIATED WITH THE ROPER-SUFFRIDGE EXTENSION OPERATOR
Danli ZHANG, Huiming XU, Jianfei WANG
Acta mathematica scientia,Series B. 2019, 39 (6):  1619-1627.  DOI: 10.1007/s10473-019-0612-9
Abstract ( 2 )   RICH HTML PDF(266KB) ( 2 )   Save
Let λG(z)|dz|be the hyperbolic metric on a simply connected proper domain G ⊂ C containing the origin, and let||·||j be the Banach norms of Cnj for j=1, 2, …, k.This note is to prove that if f is a normalized biholomorphic convex function on G, then
ΦN,1/p1,…,1/pk(f)(z)=F1/p1,…,1/pk(z)=f(z1), (f'(z1))1/p1z, …, (f'(z1))1/pkw)
is a normalized biholomorphic convex mapping on
N={(z1, z, …, w) ∈ C×Cn1×…×Cnk:||z||1p1 + … +||w||kpk<1/λG (z1)},
where N=1 + n1 + … + nk and the branch is chosen such that (f'(z1))1/pj|z1=0=1, j=1, …, k. Applying to the Roper-Suffridge extension operator, we obtain a new convex mappings construction of an unbounded domain and a refinement of convex mappings construction on a Reinhardt domain, respectively.
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ON SOLUTION TO THE NAVIER-STOKES EQUATIONS WITH NAVIER SLIP BOUNDARY CONDITION FOR THREE DIMENSIONAL INCOMPRESSIBLE FLUID
Subha PAL, Rajib HALOI
Acta mathematica scientia,Series B. 2019, 39 (6):  1628-1638.  DOI: 10.1007/s10473-019-0613-8
Abstract ( 7 )   RICH HTML PDF(278KB) ( 2 )   Save
In this article, we prove the existence and uniqueness of solutions of the Navier-Stokes equations with Navier slip boundary condition for incompressible fluid in a bounded domain of R3. The results are established by the Galerkin approximation method and improved the existing results.
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A GLOBAL EXISTENCE RESULT FOR KORTEWEG SYSTEM IN THE CRITICAL LP FRAMEWORK
Zhensheng GAO, Yan LIANG, Zhong TAN
Acta mathematica scientia,Series B. 2019, 39 (6):  1639-1660.  DOI: 10.1007/s10473-019-0614-7
Abstract ( 5 )   RICH HTML PDF(523KB) ( 6 )   Save
The purpose of this work is to investigate the initial value problem for a general isothermal model of capillary fluids derived by Dunn and Serrin[12], which can be used as a phase transition model. Motivated by[9], we aim at extending the work by Danchin-Desjardins[11] to a critical framework which is not related to the energy space. For small perturbations of a stable equilibrium state in the sense of suitable Lp-type Besov norms, we establish the global existence. As a consequence, like for incompressible flows, one may exhibit a class of large highly oscillating initial velocity fields for which global existence and uniqueness holds true.
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HARMONIC FUNCTION WITH CORRELATED COEFFICIENTS
Jacek DZIOK
Acta mathematica scientia,Series B. 2019, 39 (6):  1661-1673.  DOI: 10.1007/s10473-019-0615-6
Abstract ( 3 )   RICH HTML PDF(324KB) ( 2 )   Save
In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with varying coefficients defined by Jahangiri and Silverman. Next we define classes of harmonic functions with correlated coefficients in terms of generalized Dziok-Srivastava operator. By using extreme points theory, we obtain estimations of classical convex functionals on the defined classes of functions. Some applications of the main results are also considered.
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ON SOME SIMPLE METHODS TO DERIVE THE HAIRCLIP AND PAPERCLIP SOLUTIONS OF THE CURVE SHORTENING FLOW
Dong-Ho TSAI, Xiaoliu WANG
Acta mathematica scientia,Series B. 2019, 39 (6):  1674-1694.  DOI: 10.1007/s10473-019-0616-5
Abstract ( 4 )   RICH HTML PDF(475KB) ( 0 )   Save
We use two simple methods to derive four important explicit graphical solutions of the curve shortening flow in the plane. They are well-known as the circle, hairclip,paperclip, and grim reaper solutions of the curve shortening flow. By the methods, one can also see that the hairclip and the paperclip solutions both converge to the grim reaper solutions as t→-∞.
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ON THE LAGRANGIAN ANGLE AND THE KÄHLER ANGLE OF IMMERSED SURFACES IN THE COMPLEX PLANE C2
Xingxiao LI, Xiao LI
Acta mathematica scientia,Series B. 2019, 39 (6):  1695-1712.  DOI: 10.1007/s10473-019-0617-4
Abstract ( 4 )   RICH HTML PDF(412KB) ( 3 )   Save
In this paper, we discuss the Lagrangian angle and the Kähler angle of immersed surfaces in C2. Firstly, we provide an extension of Lagrangian angle, Maslov form and Maslov class to more general surfaces in C2 than Lagrangian surfaces, and then naturally extend a theorem by J.-M. Morvan to surfaces of constant Kähler angle, together with an application showing that the Maslov class of a compact self-shrinker surface with constant Kähler angle is generally non-vanishing. Secondly, we obtain two pinching results for the Kähler angle which imply rigidity theorems of self-shrinkers with Kähler angle under the condition that ∫M|h|2e-|x|2/2 dVM<∞, where h and x denote, respectively, the second fundamental form and the position vector of the surface.
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EPIDEMIC SPREAD ON ONE-WAY CIRCULAR-COUPLED NETWORKS
Zhongpu XU, Xinchu FU
Acta mathematica scientia,Series B. 2019, 39 (6):  1713-1732.  DOI: 10.1007/s10473-019-0618-3
Abstract ( 6 )   RICH HTML PDF(1232KB) ( 1 )   Save
Real epidemic spreading networks are often composed of several kinds of complex networks interconnected with each other, such as Lyme disease, and the interrelated networks may have different topologies and epidemic dynamics. Moreover, most human infectious diseases are derived from animals, and zoonotic infections always spread on directed interconnected networks. So, in this article, we consider the epidemic dynamics of zoonotic infections on a unidirectional circular-coupled network. Here, we construct two unidirectional three-layer circular interactive networks, one model has direct contact between interactive networks, the other model describes diseases transmitted through vectors between interactive networks, which are established by introducing the heterogeneous mean-field approach method. Then we obtain the basic reproduction numbers and stability of equilibria of the two models. Through mathematical analysis and numerical simulations, it is found that basic reproduction numbers of the models depend on the infection rates, infection periods, average degrees, and degree ratios. Numerical simulations illustrate and expand these theoretical results very well.
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STABILITY OF ε-ISOMETRIES ON L-SPACES
Duanxu DAI
Acta mathematica scientia,Series B. 2019, 39 (6):  1733-1742.  DOI: 10.1007/s10473-019-0619-2
Abstract ( 11 )   RICH HTML PDF(291KB) ( 8 )   Save
In this article, we discuss the stability of ε-isometries for L∞,λ-spaces. Indeed, we first study the relationship among separably injectivity, injectivity, cardinality injectivity and universally left stability of L∞,λ-spaces as well as we show that the second duals of universally left-stable spaces are injective, which gives a partial answer to a question of Bao-Cheng-Cheng-Dai, and then we prove a sharpen quantitative and generalized Sobczyk theorem which gives examples of nonseparable L-spaces X (but not injective) such that the couple (X, Y) is stable for every separable space Y. This gives a new positive answer to Qian's problem.
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