Acta Mathematica Scientia (Series B)
Sponsored by Wuhan Institute of Physics and
           Mathematics, CAS, China
Edited by  Editorial Committee of Acta Mathematica
           Scientia
   Add: P. O. Box 71010, Wuhan 430071, China
   Tel: 086-27-87199087(Series B)
           027-87199206(Series A & Series B)
   E-mail: actams@wipm.ac.cn
ISSN 0252-9602
CN  42-1227/O
25 October 2019, Volume 39 Issue 5 Previous Issue   
Articles
GLOBAL L SOLUTIONS TO SYSTEM OF ISENTROPIC GAS DYNAMICS IN A DIVERGENT NOZZLE WITH FRICTION
Qingyou SUN, Yunguang LU, Christian KLINGENBERG
Acta mathematica scientia,Series B. 2019, 39 (5):  1213-1218.  DOI: 10.1007/s10473-019-0501-2
In this article, we study the global L entropy solutions for the Cauchy problem of system of isentropic gas dynamics in a divergent nozzle with a friction. Especially when the adiabatic exponent γ=3, we apply for the maximum principle to obtain the L estimates w(ρδ,ε, uδ,ε) ≤ B(t) and z(ρδ,ε, uδ,ε) ≤ B(t) for the viscosity solutions (ρδ,ε, uδ,ε), where B(t) is a nonnegative bounded function for any finite time t. This work, in the special case γ ≥ 3, extends the previous works, which provided the global entropy solutions for the same Cauchy problem with the restriction w(ρδ,ε, uδ,ε) ≤ 0 or z(ρδ,ε, uδ,ε) ≤ 0.
References | Related Articles | Metrics
ON THE DIMENSIONS OF SPACES OF HARMONIC FUNCTIONS WITH POLYNOMIAL GROWTH
Xiantao HUANG
Acta mathematica scientia,Series B. 2019, 39 (5):  1219-1234.  DOI: 10.1007/s10473-019-0502-1
In this paper, we obtain an estimate for the lower bound for the dimensions of harmonic functions with polynomial growth and a Liouville type theorem on manifolds with nonnegative Ricci curvature whose tangent cone at infinity is a unique metric cone with a conic measure.
References | Related Articles | Metrics
ON SHRINKING GRADIENT RICCI SOLITONS WITH POSITIVE RICCI CURVATURE AND SMALL WEYL TENSOR
Zhuhong ZHANG, Chih-Wei CHEN
Acta mathematica scientia,Series B. 2019, 39 (5):  1235-1239.  DOI: 10.1007/s10473-019-0503-0
We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much simpler.
References | Related Articles | Metrics
SHARP HÖLDER CONTINUITY OF THE INTEGRATED DENSITY OF STATES FOR EXTENDED HARPERS MODEL WITH A LIOUVILLE FREQUENCY
Wenwen JIAN, Yunfeng SHI
Acta mathematica scientia,Series B. 2019, 39 (5):  1240-1254.  DOI: 10.1007/s10473-019-0504-z
In this article, the non-self dual extended Harper's model with a Liouville frequency is considered. It is shown that the corresponding integrated density of states is 1/2-Hölder continuous. As an application, the homogeneity of the spectrum is proven.
References | Related Articles | Metrics
GRADIENT ESTIMATES FOR THE COMMUTATOR WITH FRACTIONAL DIFFERENTIATION FOR SECOND ORDER ELLIPTIC OPERATORS
Wenyu TAO, Yanping CHEN, Jili LI
Acta mathematica scientia,Series B. 2019, 39 (5):  1255-1264.  DOI: 10.1007/s10473-019-0505-y
Let L=-div(A∇) be a second order divergence form elliptic operator, where A is an accretive, n×n matrix with bounded measurable complex coefficients on Rn. Let Lα/2 (0 < α < 1) denotes the fractional differential operator associated with L and (-∆)α/2bLn/α(Rn). In this article, we prove that the commutator[b, Lα/2] is bounded from the homogenous Sobolev space Lα2 (Rn) to L2(Rn).
References | Related Articles | Metrics
SHARP ESTIMATES OF QUASI-CONVEX MAPPINGS OF TYPE B AND ORDER α
Mingsheng LIU, Fen WU, Yan YANG
Acta mathematica scientia,Series B. 2019, 39 (5):  1265-1276.  DOI: 10.1007/s10473-019-0506-x
In this paper, we first establish several sharp inequalities of homogeneous expansion for biholomorphic quasi-convex mappings of type B and order α on the unit ball E in a complex Banach space X by applying the method and technique of complex analysis. Then, as the application of these sharp inequalities, we derive the sharp estimate of third homogeneous expansions for the above mappings defined on the unit polydisk Un in Cn.
References | Related Articles | Metrics
ON FIXED POINTS OF MEROMORPHIC FUNCTIONS f(z) AND f(z + c),∆cf(z)
Shuangting LAN, Zongxuan CHEN
Acta mathematica scientia,Series B. 2019, 39 (5):  1277-1289.  DOI: 10.1007/s10473-019-0507-9
Let c be a nonzero constant and f(z) be a transcendental meromorphic function of finite order. Under some conditions, we study the relationships between the exponent of convergence of fixed points of f(z), its shift f(z +c) and forward differences ∆cn f(z), n ∈ N+.
References | Related Articles | Metrics
GLOBAL EXISTENCE, EXPONENTIAL DECAY AND BLOW-UP IN FINITE TIME FOR A CLASS OF FINITELY DEGENERATE SEMILINEAR PARABOLIC EQUATIONS
Hua CHEN, Huiyang XU
Acta mathematica scientia,Series B. 2019, 39 (5):  1290-1308.  DOI: 10.1007/s10473-019-0508-8
In this paper, we study the initial-boundary value problem for the semilinear parabolic equations ut -△Xu=|u|p-1u, where X=(X1, X2, …, Xm) is a system of real smooth vector fields which satisfy the H?rmander's condition, and is a finitely degenerate elliptic operator. Using potential well method, we first prove the invariance of some sets and vacuum isolating of solutions. Finally, by the Galerkin method and the concavity method we show the global existence and blow-up in finite time of solutions with low initial energy or critical initial energy, and also we discuss the asymptotic behavior of the global solutions.
References | Related Articles | Metrics
THE APPROXIMATION SOLUTIONS FOR HIGHER DIMENSIONAL INTEGRO-DIFFERENTIAL EQUATIONS
Lüping CHEN
Acta mathematica scientia,Series B. 2019, 39 (5):  1309-1318.  DOI: 10.1007/s10473-019-0509-7
This work deals with approximation solutions to a type of integro-differential equations in several complex variables. It concerns the Cauchy formula on higher dimensional domains. In our study, we make use of multiple power series expansions and an iterative computation method to solve a kind of integro-differential equation. We introduce a symmetrized topology product area which is called a bicylinder. We expand functions and derivatives of them to power series. Moreover we obtain unknown functions by comparing coefficients of the series on both sides of equations. We express the approximation solutions by a regular product of matrixes.
References | Related Articles | Metrics
ON BONNESEN-STYLE SYMMETRIC MIXED ISOHOMOTHETIC INEQUALITY IN R2
Yuanyuan WANG, Xingxing WANG, Chunna ZENG
Acta mathematica scientia,Series B. 2019, 39 (5):  1319-1329.  DOI: 10.1007/s10473-019-0510-1
In this paper, we investigate the translative containment measure for a convex domain Ki to contain, or to be contained in the homothetic copy of another convex domain tKj(t ≥ 0). Via the formulas of translative Blaschke and Poincaré in integral formula, we obtain a Bonnesen-style symmetric mixed isohomothetic inequality. The Bonnesen-style symmetric mixed isohomothetic inequality obtained is known as Bonnesen-style inequality if one of the domains is a disc. As a direct consequence, we attain an inequality which strengthen the result proved by Bonnesen, Blaschké and Flanders. Furthermore, by the containment measure and Blaschke's rolling theorem, we obtain the reverse Bonnesen-style symmetric mixed isohomothetic inequalities. These inequalities are the analogues of the known Bottema's result in 1933.
References | Related Articles | Metrics
THE APPROXIMATION PROPERTY OF GENERALIZED FIGÀ-TALAMANCA-HERZ ALGEBRAS
Cheng YAN
Acta mathematica scientia,Series B. 2019, 39 (5):  1330-1338.  DOI: 10.1007/s10473-019-0511-0
Let G be a discrete group with a weight w on it. For p>1, we define a class of generalized Figà-Talamanca-Herz algebras Ap(G, w, α, θ) and obtain their (w, α, θ)-Dual spaces. Moreover, we show that the generalized Figà-Talamanca-Herz algebras have an approximation property when G is a proper discrete group and satisfies the p-RD property.
References | Related Articles | Metrics
A SCHWARZ LEMMA FOR HARMONIC FUNCTIONS IN THE REAL UNIT BALL
Shaoyu DAI, Huaihui CHEN
Acta mathematica scientia,Series B. 2019, 39 (5):  1339-1344.  DOI: 10.1007/s10473-019-0512-z
We establish a precise Schwarz lemma for real-valued and bounded harmonic functions in the real unit ball of dimension n. This extends Chen's Schwarz-Pick lemma for real-valued and bounded planar harmonic mapping.
References | Related Articles | Metrics
ASYMPTOTIC PROPERTIES OF A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME
Yuejiao WANG, Zaiming LIU, Quansheng LIU, Yingqiu LI
Acta mathematica scientia,Series B. 2019, 39 (5):  1345-1362.  DOI: 10.1007/s10473-019-0513-y
We consider a branching random walk in an independent and identically distributed random environment ξ=(ξn) indexed by the time. Let W be the limit of the martingale Wn=∫e-txZn(dx)/Eξ ∫e-txZn(dx), with Zn denoting the counting measure of particles of generation n, and Eξ the conditional expectation given the environment ξ. We find necessary and sufficient conditions for the existence of quenched moments and weighted moments of W, when W is non-degenerate.
References | Related Articles | Metrics
BOUNDARY BLOW-UP RATE OF THE LARGE SOLUTION FOR AN ELLIPTIC COOPERATIVE SYSTEM
Ying WANG, Mingxin WANG
Acta mathematica scientia,Series B. 2019, 39 (5):  1363-1379.  DOI: 10.1007/s10473-019-0514-x
In this article we consider positive large solution of cooperative systems of the form -∆u1=λ1u1 + a1u1u2q1 -b1(x)u1p1+1, -∆u2=λ2u2 + a2u1q2u2 -b2(x)u2p2+1 in a bounded smooth domain Ω ⊂ RN(λiR, ai, bi>0, 0 < qi < pj, i, j ∈ {1, 2}, ij), Based on the construction of certain sup and sub-solution, we show existence, uniqueness and blow-up rate of the large solution.
References | Related Articles | Metrics
SOLVABILITY OF A NONLINEAR PROBLEM ARISING IN REACTIONS OVER INHOMOGENEOUS SURFACES
Vladas SKAKAUSKAS
Acta mathematica scientia,Series B. 2019, 39 (5):  1380-1396.  DOI: 10.1007/s10473-019-0515-9
The existence and uniqueness theorem of classical solutions of a coupled system of nonlinear parabolic PDEs arising in modelling of chemical reactions between two polymeric reactants over inhomogeneous surfaces with nonclassical boundary conditions is proved and the long-time behaviour of the solution is studied.
References | Related Articles | Metrics
ON THE HEAT FLOW OF EQUATION OF H-SURFACE
Guochun WU, Zhong TAN, Jiankai XU
Acta mathematica scientia,Series B. 2019, 39 (5):  1397-1405.  DOI: 10.1007/s10473-019-0516-8
We study the heat flow of equation of H-surface with non-zero Dirichlet boundary in the present article. Introducing the "stable set" M2 and "unstable set" M1, we show that there exists a unique global solution provided the initial data belong to M2 and the global solution converges to zero in H1 exponentially as time goes to infinity. Moreover, we also prove that the local regular solution must blow up at finite time provided the initial data belong to M1.
References | Related Articles | Metrics
UNILATERAL BIFURCATION FOR SEVERAL-PARAMETER EIGENVALUE PROBLEM WITH HOMOGENEOUS OPERATOR
Xiaofei CAO, Guowei DAI
Acta mathematica scientia,Series B. 2019, 39 (5):  1406-1414.  DOI: 10.1007/s10473-019-0517-7
We establish the unilateral global bifurcation result for the following nonlinear operator equation
u=L(λ)u + H(λ, u), (λ, u) ∈ Rm×X
where m is a positive integer, X is a Banach space, L(·) is a positively homogeneous completely continuous operator and H:Rm×XX is completely continuous with H=o (||u||) near u=0 uniformly on bounded λ sets.
References | Related Articles | Metrics
A NOTE ON g-CONCAVE FUNCTION
Guangyan JIA, Yuhong XU
Acta mathematica scientia,Series B. 2019, 39 (5):  1415-1422.  DOI: 10.1007/s10473-019-0518-6
An equivalent condition is derived for g-concave function defined by (static) g-expectation. Several extensions including quadratic generators and (g,h)-concavity are also considered.
References | Related Articles | Metrics
INVERSE PROBLEM STABILITY OF A CONTINUOUS-IN-TIME FINANCIAL MODEL
Tarik CHAKKOUR
Acta mathematica scientia,Series B. 2019, 39 (5):  1423-1439.  DOI: 10.1007/s10473-019-0519-5
In this work, we study the inverse problem stability of the continuous-in-time model which is designed to be used for the finances of public institutions. We discuss this study with determining the Loan measure from algebraic spending measure in Radon measure space M([tI, Θmax]), and in Hilbert space L2([tI, Θmax]) when they are density measures. For this inverse problem we prove the uniqueness theorem, obtain a procedure for constructing the solution and provide necessary and sufficient conditions for the solvability of the inverse problem in L2([tI, Θmax]).
References | Related Articles | Metrics
MONOTONICITY, CONVEXITY AND INEQUALITIES INVOLVING THE GENERALIZED ELLIPTIC INTEGRALS
Miaokun WANG, Wen ZHANG, Yuming CHU
Acta mathematica scientia,Series B. 2019, 39 (5):  1440-1450.  DOI: 10.1007/s10473-019-0520-z
We establish the monotonicity and convexity properties for several special functions involving the generalized elliptic integrals, and present some new analytic inequalities.
References | Related Articles | Metrics
GROUND STATE SOLUTIONS FOR THE CRITICAL KLEIN-GORDON-MAXWELL SYSTEM
Lixia WANG, Xiaoming WANG, Luyu ZHANG
Acta mathematica scientia,Series B. 2019, 39 (5):  1451-1460.  DOI: 10.1007/s10473-019-0521-y

 

In this article, we study the following Klein-Gordon-Maxwell system involving critical exponent
(KGM)

where λ and ω are two positive constants. We found the existence of positive ground state solutions (that is, for solutions which minimizes the action functional among all the solutions) of (KGM) which improves some previous existence result in Carri?o et al.(2012)[8].

References | Related Articles | Metrics