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    1. DECAY ESTIMATE AND GLOBAL EXISTENCE OF SEMILINEAR THERMOELASTIC TIMOSHENKO SYSTEM WITH TWO DAMPING EFFECTS
    王维克, 薛锐
    数学物理学报(英文版)    2019, 39 (6): 1461-1486.   DOI: 10.1007/s10473-019-0601-z
    摘要125)      PDF       收藏
    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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    2. HILBERT PROBLEM 15 AND NONSTANDARD ANALYSIS (I)
    李邦河
    数学物理学报(英文版)    2020, 40 (1): 1-15.   DOI: 10.1007/s10473-020-0101-4
    摘要71)      PDF       收藏
    In this article, we consider the following coupled fractional nonlinear Schr?dinger system in $\mathbb{R}^{N}$ \[\left\{ \begin{array}{l} {\left( { - \Delta } \right)^s}u + P\left( x \right)u = {\mu _1}{\left| u \right|^{2p - 2}}u + \beta {\left| u \right|^p}{\left| u \right|^{p - 2}}u,\;\;\;x \in {{\mathbb{R}}^N},\\{\left( { - \Delta } \right)^s}v + Q\left( x \right)v = {\mu _2}{\left| v \right|^{2p - 2}}v + \beta {\left| v \right|^p}{\left| v \right|^{p - 2}}v,\;\;\;\;\;x \in {{\mathbb{R}}^N},\\u,\;\;v \in {H^s}\left( {{{\mathbb{R}}^N}} \right),\end{array} \right.\] where $N≥2, 0 < s < 1, 1 < p < \frac{N}{N-2s},\mu_1>0, \mu_2>0$ and $\beta \in \mathbb{R}$ is a coupling constant. We prove that it has infinitely many non-radial positive solutions under some additional conditions on $P(x), Q(x), p$ and $\beta$. More precisely, we will show that for the attractive case, it has infinitely many non-radial positive synchronized vector solutions, and for the repulsive case, infinitely many non-radial positive segregated vector solutions can be found, where we assume that $P(x)$ and $Q(x)$ satisfy some algebraic decay at infinity.
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    3. SYMMETRY OF POSITIVE SOLUTIONS FOR THE FRACTIONAL HARTREE EQUATION
    刘祥清
    数学物理学报(英文版)    2019, 39 (6): 1508-1516.   DOI: 10.1007/s10473-019-0603-x
    摘要60)      PDF       收藏
    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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    4. THE SCHWARZ LEMMA AT THE BOUNDARY OF THE NON-CONVEX COMPLEX ELLIPSOIDS
    何乐, 涂振汉
    数学物理学报(英文版)    2019, 39 (4): 915-926.   DOI: 10.1007/s10473-019-0401-5
    摘要58)      PDF       收藏
    Let B2,p:={z∈C2:|z1|2+|z2|p<1} (0 < p < 1). Then, B2,p (0 < p < 1) is a non-convex complex ellipsoid in C2 without smooth boundary. In this article, we establish a boundary Schwarz lemma at z0 ∈ ∂B2,p for holomorphic self-mappings of the non-convex complex ellipsoid B2,p, where z0 is any smooth boundary point of B2,p.
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    5. SHUBIN REGULARITY FOR THE RADIALLY SYMMETRIC SPATIALLY HOMOGENEOUS BOLTZMANN EQUATION WITH DEBYE-YUKAWA POTENTIAL
    Léo GLANGETAS, 李浩光
    数学物理学报(英文版)    2019, 39 (6): 1487-1507.   DOI: 10.1007/s10473-019-0602-y
    摘要51)      PDF       收藏
    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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    6. GLOBAL L SOLUTIONS TO SYSTEM OF ISENTROPIC GAS DYNAMICS IN A DIVERGENT NOZZLE WITH FRICTION
    孙庆有, 陆云光, Christian KLINGENBERG
    数学物理学报(英文版)    2019, 39 (5): 1213-1218.   DOI: 10.1007/s10473-019-0501-2
    摘要46)      PDF       收藏
    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.
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    7. INFINITE SERIES FORMULAE RELATED TO GAUSS AND BAILEY $_2F_1(\tfrac12)$-SUMS
    初文昌
    数学物理学报(英文版)    2020, 40 (2): 293-315.   DOI: 10.1007/s10473-020-0201-y
    摘要42)      PDF       收藏
    The unified Ω-series of the Gauss and Bailey $_2F_1(\tfrac12)$-sums will be investigated by utilizing asymptotic methods and the modified Abel lemma on summation by parts. Several remarkable transformation theorems for the Ω-series will be proved whose particular cases turn out to be strange evaluations of nonterminating hypergeometric series and infinite series identities of Ramanujan-type, including a couple of beautiful expressions for π and the Catalan constant discovered by Guillera (2008).
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    8. INFINITELY MANY SOLITARY WAVES DUE TO THE SECOND-HARMONIC GENERATION IN QUADRATIC MEDIA
    王春花, 周静
    数学物理学报(英文版)    2020, 40 (1): 16-34.   DOI: 10.1007/s10473-020-0102-3
    摘要40)      PDF       收藏

    In this paper, we consider the following coupled Schr?dinger system with χ(2) nonlinearities

    which arises from second-harmonic generation in quadratic media. Here V1(x) and V2(x) are radially positive functions, 2 ≤ N < 6, α > 0 and α > β. Assume that the potential functions V1(x) and V2(x) satisfy some algebraic decay at infinity. Applying the finite dimensional reduction method, we construct an unbounded sequence of non-radial vector solutions of synchronized type.

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    9. COMPLEX SYMMETRIC TOEPLITZ OPERATORS ON THE UNIT POLYDISK AND THE UNIT BALL
    蒋操, 董兴堂, 周泽华
    数学物理学报(英文版)    2020, 40 (1): 35-44.   DOI: 10.1007/s10473-020-103-2
    摘要36)      PDF       收藏
    In this article, we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables. Surprisingly, the necessary and sufficient conditions for Toeplitz operators to be complex symmetric on these two spaces with certain conjugations are just the same. Also, some interesting symmetry properties of complex symmetric Toeplitz operators are obtained.
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    10. MULTI-BUMP SOLUTIONS FOR NONLINEAR CHOQUARD EQUATION WITH POTENTIAL WELLS AND A GENERAL NONLINEARITY
    郭伦, 胡亭曦
    数学物理学报(英文版)    2020, 40 (2): 316-340.   DOI: 10.1007/s10473-020-0202-x
    摘要36)      PDF       收藏
    In this article, we study the existence and asymptotic behavior of multi-bump solutions for nonlinear Choquard equation with a general nonlinearity \begin{equation*} -\Delta u+(\lambda a(x)+1)u=\Big(\frac{1}{|x|^{\alpha}}\ast F(u)\Big)f(u) \ \ \text{in}\ \ \mathbb{R}^{N}, \end{equation*} where $N\geq 3$, $0<\alpha< \min\{N,4\}$, $\lambda$ is a positive parameter and the nonnegative potential function $a(x)$ is continuous. Using variational methods, we prove that if the potential well int$(a^{-1}(0))$ consists of $k$ disjoint components, then there exist at least $2^k-1$ multi-bump solutions. The asymptotic behavior of these solutions is also analyzed as $\lambda\to +\infty$.
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    11. GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR SOME COUPLED SYSTEMS VIA A LYAPUNOV FUNCTIONAL
    Lamia DJEBARA, Salem ABDELMALEK, Samir BENDOUKHA
    数学物理学报(英文版)    2019, 39 (6): 1538-1550.   DOI: 10.1007/s10473-019-0606-7
    摘要35)      PDF       收藏
    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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    12. A STUDY OF A FULLY COUPLED TWO-PARAMETER SYSTEM OF SEQUENTIAL FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL INTEGRO-MULTIPOINT BOUNDARY CONDITIONS
    Ahmed ALSAEDI, Bashir AHMAD, Shorog ALJOUDI, Sotiris K. NTOUYAS
    数学物理学报(英文版)    2019, 39 (4): 927-944.   DOI: 10.1007/s10473-019-0402-4
    摘要32)      PDF       收藏
    In this article, we discuss the existence and uniqueness of solutions for a coupled two-parameter system of sequential fractional integro-differential equations supplemented with nonlocal integro-multipoint boundary conditions. The standard tools of the fixed-point theory are employed to obtain the main results. We emphasize that our results are not only new in the given configuration, but also correspond to several new special cases for specific values of the parameters involved in the problem at hand.
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    13. STABILITY OF ε-ISOMETRIES ON L-SPACES
    戴端旭
    数学物理学报(英文版)    2019, 39 (6): 1733-1742.   DOI: 10.1007/s10473-019-0619-2
    摘要31)      PDF       收藏
    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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    14. THE BOUNDEDNESS FOR COMMUTATORS OF ANISOTROPIC CALDERÓN-ZYGMUND OPERATORS
    李金霞, 李宝德, 何建勋
    数学物理学报(英文版)    2020, 40 (1): 45-58.   DOI: 10.1007/s10473-020-104-1
    摘要30)      PDF       收藏
    Let T be an anisotropic Calderón-Zygmund operator and φ : Rn×[0, ∞) → [0, ∞) be an anisotropic Musielak-Orlicz function with φ(x, ·) being an Orlicz function and φ(·, t) being a Muckenhoupt A(A) weight. In this paper, our goal is to study two boundedness theorems for commutators of anisotropic Calderón-Zygmund operators. Precisely, when b ∈ BMOw(Rn, A) (a proper subspace of anisotropic bounded mean oscillation space BMO(Rn, A)), the commutator [b, T] is bounded from anisotropic weighted Hardy space Hw1(Rn, A) to weighted Lebesgue space Lw1(Rn) and when b ∈ BMO(Rn) (bounded mean oscillation space), the commutator [b, T] is bounded on Musielak-Orlicz space Lφ(Rn), which are extensions of the isotropic setting.
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    15. EPIDEMIC SPREAD ON ONE-WAY CIRCULAR-COUPLED NETWORKS
    徐忠朴, 傅新楚
    数学物理学报(英文版)    2019, 39 (6): 1713-1732.   DOI: 10.1007/s10473-019-0618-3
    摘要29)      PDF       收藏
    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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    16. GLOBAL EXISTENCE AND DECAY ESTIMATES FOR THE CLASSICAL SOLUTIONS TO A COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL
    丁时进, 黄丙远, 黎泉荣
    数学物理学报(英文版)    2019, 39 (6): 1525-1537.   DOI: 10.1007/s10473-019-0605-8
    摘要25)      PDF       收藏
    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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    17. NEW RESULTS FOR A CLASS OF UNIVALENT FUNCTIONS
    彭志刚, Milutin OBRADOVI?
    数学物理学报(英文版)    2019, 39 (6): 1579-1588.   DOI: 10.1007/s10473-019-0609-4
    摘要25)      PDF       收藏
    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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    18. STABILITY OF MONOSTABLE WAVES FOR A NONLOCAL EQUATION WITH DELAY AND WITHOUT QUASI-MONOTONICITY
    刘克盼, 杨赟瑞, 杨扬
    数学物理学报(英文版)    2019, 39 (6): 1589-1604.   DOI: 10.1007/s10473-019-0610-y
    摘要24)      PDF       收藏
    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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    19. ON THE DIMENSIONS OF SPACES OF HARMONIC FUNCTIONS WITH POLYNOMIAL GROWTH
    黄显涛
    数学物理学报(英文版)    2019, 39 (5): 1219-1234.   DOI: 10.1007/s10473-019-0502-1
    摘要24)      PDF       收藏
    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.
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    20. THE ORLICZ BRUNN-MINKOWSKI INEQUALITY FOR DUAL HARMONIC QUERMASSINTEGRALS
    吴翔, 李寿贵
    数学物理学报(英文版)    2019, 39 (4): 945-954.   DOI: 10.1007/s10473-019-0403-3
    摘要24)      PDF       收藏
    Within the framework of Orlicz Brunn-Minkowski theory recently introduced by Lutwak, Yang, and Zhang[20, 21], Gardner, Hug, and Weil[5, 6] et al, the dual harmonic quermassintegrals of star bodies are studied, and a new Orlicz Brunn-Minkowski type inequality is proved for these geometric quantities.
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