数学物理学报(英文版)

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EXISTENCE OF ENTROPY SOLUTIONS TO TWO-DIMENSIONAL STEADY EXOTHERMICALLY REACTING EULER EQUATIONS

陈贵强, 肖长国, 张永前

数学物理学报(英文版). 2014 (1): 1-38. DOI: 10.1016/S0252-9602(13)60123-X

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We are concerned with the global existence of entropy solutions of the twodimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function (T) is assumed to have a positive lower bound. We first consider the Cauchy problem (the initial value problem), that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an additional
detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave (weak or strong, determined by the wedge angle at the wedge vertex) when the total variation of both the slope of the wedge boundary and
the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.

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GLOBAL EXISTENCE OF CLASSICAL SOLUTION FOR A VISCOUS LIQUID-GAS TWO-PHASE MODEL WITH MASS-DEPENDENT VISCOSITY AND VACUUM

王振, 张卉

数学物理学报(英文版). 2014 (1): 39-52. DOI: 10.1016/S0252-9602(13)60124-1

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In this work, we obtain the global existence and uniqueness of classical solu-tions to a viscous liquid-gas two-phase model with mass-dependent viscosity and vacuum in one dimension, where the initial vacuum is allowed. We get the upper and lower bounds of gas and liquid masses n and m by the continuity methods which we use to study the
compressible Navier-Stokes equations.

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GENERALIZED FRACTIONAL TRACE VARIATIONAL IDENTITY AND A NEW FRACTIONAL INTEGRABLE COUPLINGS#br# OF SOLITON HIERARCHY

魏含玉, 夏铁成

数学物理学报(英文版). 2014 (1): 53-64. DOI: 10.1016/S0252-9602(13)60125-3

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Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian
structures of the fractional integrable couplings of the soliton hierarchy.

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QUASI-SURE CONVERGENCE RATE OF EULER SCHEME FOR STOCHASTIC DIFFERENTIAL EQUATIONS

黄文亮, 张希承

数学物理学报(英文版). 2014 (1): 65-72. DOI: 10.1016/S0252-9602(13)60126-5

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Let X_t(x) be the solution of stochastic differential equations with smooth and bounded derivatives coefficients. Let Xⁿ_t(x) be the Euler discretization scheme of SDEs with step 2⁻ⁿ. In this note, we prove that for any R > 0 and γ∈ (0, 1/2),
sup_{t∈[0,1],|x|≤R}|Xⁿ_t(x, ω) − X_t(x, ω)| ξ _R, γ(ω)2^−nγ, n > 1, q.e.,
where ξ_{R, γ}(ω) is quasi-everywhere finite.

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COMPOSITION OPERATORS BETWEEN BLOCH TYPE SPACES IN THE UNIT BALL

戴济能, 欧阳才衡

数学物理学报(英文版). 2014 (1): 73-81. DOI: 10.1016/S0252-9602(13)60127-7

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In this paper, we obtain some new necessary and sufficient conditions for the boundedness and compactness of composition operators C_Φ between Bloch type spaces in the unit ball Bⁿ.

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ON AN INFINITE FAMILY IN π_*S

刘秀贵

数学物理学报(英文版). 2014 (1): 82-92. DOI: 10.1016/S0252-9602(13)60128-9

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In this paper, a new family of homotopy elements in the stable homotopy groups of spheres represented by h1hnhm˜
s in the Adams spectral sequence is detected, where n − 2 ≥ m ≥ 5 and 3 ≤ s < p.

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GLOBAL EXISTENCE AND CONVERGENCE RATES OF SMOOTH SOLUTIONS FOR THE 3-D COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITHOUT HEAT CONDUCTIVITY

高真圣, 谭忠, 吴国春

数学物理学报(英文版). 2014 (1): 93-106. DOI: 10.1016/S0252-9602(13)60129-0

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In this paper, we are concerned with the global existence and convergence rates of the smooth solutions for the compressible magnetohydrodynamic equations without heat conductivity, which is a hyperbolic-parabolic system. The global solutions are obtained by combining the local existence and a priori estimates if H³-norm of the initial perturbation around a constant states is small enough and its L¹-norm is bounded. A priori decay-in-time estimates on the pressure, velocity and magnetic field are used to get the uniform bound of entropy. Moreover, the optimal convergence rates are also obtained.

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WELL-POSEDNESS OF A COMPRESSIBLE GAS-LIQUID MODEL FOR DEEPWATER OIL WELL OPERATIONS

Helmer A. FRIIS, Steinar EVJE

数学物理学报(英文版). 2014 (1): 107-124. DOI: 10.1016/S0252-9602(13)60130-7

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The main purpose of this paper is two-fold: (i) to generalize an existence result for a compressible gas-liquid model with a friction term recently published by Friis and Evje [SIAM J. Appl. Math., 71 (2011), pp. 2014–2047]; (ii) to derive a uniqueness result for the same model. A main ingredient in the existence part is the observation that we can consider weaker assumptions on the initial liquid and gas mass, and still obtain an existence result. Compared to the above mentioned work, we rely on a more refined application of the estimates provided by the basic energy estimate. Concerning the uniqueness result, we borrow ideas from Fang and Zhang [Nonlinear Anal. TMA, 58 (2004), pp. 719–731] and derive a stability result under appropriate constraints on parameters that determine rate of decay toward zero at the boundary for gas and liquid masses, and growth rate of masses associated with the friction term and viscous coefficient.

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STABILITY OF DISPLACEMENT TO THE SECOND FUNDAMENTAL PROBLEM IN PLANE ELASTICITY

林娟, 杜金元

数学物理学报(英文版). 2014 (1): 125-140. DOI: 10.1016/S0252-9602(13)60131-9

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In this article, by using the stability of Cauchy type integral when the smooth perturbation for integral curve and the Sobolev type perturbation for kernel density hap-pen, we discuss the stability of the second fundamental problem in plane elasticity when the smooth perturbation for the boundary of the elastic domain (unit disk) and the Sobolev type perturbation for the displacement happen. And the error estimate of the displacement between the second fundamental problem and its perturbed problem is obtained.

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ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES

陈振龙

数学物理学报(英文版). 2014 (1): 141-161. DOI: 10.1016/S0252-9602(13)60132-0

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Let X⁽¹⁾ = {X⁽¹⁾(s), s ∈ R₊} and X⁽²⁾ = {X⁽²⁾(t), t ∈ R₊} be two inde-pendent nondegenerate diffusion processes with values in R^d. The existence and fractal dimension of intersections of the sample paths of X⁽¹⁾ and X⁽²⁾ are studied. More gener-ally, let E₁, E₂ ⊆ (0, ∞) and F ⊂ R^d be Borel sets. A necessary condition and a sufficient condition for P{X⁽¹⁾(E₁) ∩X⁽²⁾(E₂) ∩F 6≠Φ} > 0 are proved in terms of the Bessel-Riesz type capacity and Hausdorff measure of E₁×E₂×F in the metric space (R₊×R₊×R^d, ρ), where ρ is an unsymmetric metric defined in R₊ ×R₊ ×R^d. Under reasonable conditions, results resembling those of Browian motion are obtained.

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NOTES ON THE RESCALED SASAKI TYPE METRIC ON THE COTANGENT BUNDLE

Aydin GEZER, Murat ALTUNBAS

数学物理学报(英文版). 2014 (1): 162-174. DOI: 10.1016/S0252-9602(13)60133-2

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Let (M, g) be an n-dimensional Riemannian manifold and T*M be its cotan-gent bundle equipped with the rescaled Sasaki type metric. In this paper, we firstly study the paraholomorphy property of the rescaled Sasaki type metric by using some compati-ble paracomplex structures on T*M. Second, we construct locally decomposable Golden Riemannian structures on T*M. Finally we investigate curvature properties of T*M.

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ON GENERALIZED ORDERS AND GENERALIZED TYPES OF DIRICHLET SERIES IN THE RIGHT HALF-PLANE

霍颖莹, 孔荫莹

数学物理学报(英文版). 2014 (1): 175-182. DOI: 10.1016/S0252-9602(13)60134-4

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In the paper, generalized orders and generalized types of Dirichlet series in the right half-plane are given. Some interesting relationships on maximum modulus, the maximum term and the coefficients of entire function defined by Dirichlet series of in the right half-plane are obtained.

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HOMOGENIZATION OF THE INCOMPRESSIBLE NAVIER-STOKES FLUID WITH OSCILLATION COEFFICIENT

赵红星

数学物理学报(英文版). 2014 (1): 183-193. DOI: 10.1016/S0252-9602(13)60135-6

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We study the homogenization of the incompressible Navier-Stokes equations with periodic oscillating coefficient in a bounded non-homogeneous media. To do that, we introduce a generalized compensate compactness result and a suitable class of test function to this problem. By passing the limit, we obtain the homogenized model of this problem.

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A NOTE ON n-PERINORMAL OPERATORS

左红亮, 左飞

数学物理学报(英文版). 2014 (1): 194-198. DOI: 10.1016/S0252-9602(13)60136-8

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The study of operators satisfying σ_ja(T) = σ_a(T) is of significant interest. Does σ_ja(T) = σ_a(T) for n-perinormal operator T ∈B(H)? This question was raised by Mecheri and Braha [Oper. Matrices 6 (2012), 725–734]. In the note we construct a
counterexample to this question and obtain the following result: if T is a n-perinormal operator in B(H), then σ_ja(T)\{0} = σ_a(T)\{0}. We also consider tensor product of n-perinormal operators.

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LOCAL WELL-POSEDNESS IN SOBOLEV SPACES WITH NEGATIVE INDICES FOR A SEVENTH ORDER DISPERSIVE EQUATION

王宏伟

数学物理学报(英文版). 2014 (1): 199-208. DOI: 10.1016/S0252-9602(13)60137-X

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This paper is concerned with the Cauchy problem of a seventh order dispersive equation. We prove local well-posedness with initial data in Sobolev spaces H^s(R) for negative indices of s > −11/4 .

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THE MAXIMAL NUMBER OF I_π-CHARACTERS OVER NORMAL SUBGROUPS

周芳, 米芳, 刘合国

数学物理学报(英文版). 2014 (1): 209-214. DOI: 10.1016/S0252-9602(13)60138-1

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Let G be a π-separable group for a set of primes, let N be a normal subgroup of G, and let θ be an I_π-character (i.e., irreducible π-partial character) of N. We obtain a necessary and sufficient condition for the number of I_πcharacters of G over θ to take the possible maximum |G : N|_π. Some applications are given.

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THE PROLONGATION STRUCTURES AND NONLOCAL SYMMETRIES FOR MODIFIED BOUSSINESQ SYSTEM

程秋盛, 贺劲松

数学物理学报(英文版). 2014 (1): 215-227. DOI: 10.1016/S0252-9602(13)60139-3

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The Wahlquist-Estabrook (WE) prolongation structures of modified Boussi-nesq (MB) system are studied from the coverings point of view. The realizations and classifications of one-dimensional coverings of this system are obtained completely. More-over the sufficient and necessary conditions for a vector field to be a nonlocal symmetry of this system are also demonstrated in the WE prolongation structures.

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ON THE COEFFICIENTS OF SEVERAL CLASSES OF BI-UNIVALENT FUNCTIONS

彭志刚, 韩秋秋

数学物理学报(英文版). 2014 (1): 228-240. DOI: 10.1016/S0252-9602(13)60140-X

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In this paper, we investigate the bounds of the coefficients of several classes of bi-univalent functions. The results presented in this paper improve or generalize the recent works of other authors.

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