数学物理学报(英文版)

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1. EXISTENCE OF SOLUTION FOR A BOUNDARY VALUE PROBLEM OF FRACTIONAL ORDER

张淑琴

数学物理学报(英文版) DOI: 10.1016/S0252-9602(06)60044-1

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2. A RISK-SENSITIVE STOCHASTIC MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL OF JUMP DIFFUSIONS AND ITS APPLICATIONS

史敬涛, 吴臻

数学物理学报(英文版) 2011, 31 (2): 419-433. DOI: 10.1016/S0252-9602(11)60242-7

摘要（731）

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A stochastic maximum principle for the risk-sensitive optimal control problem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained.

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3. MULTIPLE SOLUTIONS FOR THE p&q-LAPLACIAN PROBLEM WITH CRITICAL EXPONENT

李工宝, 张国

数学物理学报(英文版) 2009, 29 (4): 903-918. DOI: 10.1016/S0252-9602(09)60077-1

摘要（1027）

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In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p&q-Laplacian type involving the critical Sobolev exponent:

−△_pu − △_qu = |u|^p*−2u + μ|u|^r−2u in Ω,
u|∂Ω= 0,

where Ω ⊂ R^N is a bounded domain, N > p, p* = N_p /N−p is the critical Sobolev exponent and μ > 0. We prove that if 1 < r < q < p < N, then there is a μ₀ > 0, such that for any μ ∈ (0, μ₀), the above mentioned problem possesses infinitely many weak solutions. Our result generalizes a similar result in [8] for p-Laplacian type problem.

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4. L² DECAY OF THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DAMPING

蔡晓静, 雷利华

数学物理学报(英文版) 2010, 30 (4): 1235-1248. DOI: 10.1016/S0252-9602(10)60120-8

摘要（870）

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In this article, we show large time behavior of weak solutions to the Cauchy problem of the Navier-Stokes equations with damping α|u|^β-1u (α>0).

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5. EXACT NULL CONTROLLABILITY OF NON-AUTONOMOUS FUNCTIONAL EVOLUTION SYSTEMS WITH NONLOCAL CONDITIONS

傅显隆, 张玉

数学物理学报(英文版) 2013, 33 (3): 747-757. DOI: 10.1016/S0252-9602(13)60035-1

摘要（283）

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In this article, by using theory of linear evolution system and Schauder fixed point theorem, we establish a sufficient result of exact null controllability for a non-autonomous functional evolution system with nonlocal conditions. In particular, the compactness condi-tion or Lipschitz condition for the function g in the nonlocal conditions appearing in various
literatures is not required here. An example is also provided to show an application of the obtained result.

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6. 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, 34 (1): 93-106. DOI: 10.1016/S0252-9602(13)60129-0

摘要（200）

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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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7. ASYMPTOTIC STABILITY OF RAREFACTION WAVE FOR HYPERBOLIC-ELLIPTIC COUPLED SYSTEM IN RADIATING GAS

阮立志; 张晶

数学物理学报(英文版) DOI: 10.1016/S0252-9602(07)60035-6

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8. MULTI-DIMENSIONAL GEOMETRIC BROWNIAN MOTIONS, ONSAGER-MACHLUP FUNCTIONS, AND APPLICATIONS TO MATHEMATICAL FINANCE

胡耀忠

数学物理学报(英文版) 2000, 20 (3): 341-358.

摘要（958）

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The solutions of the following bilinear stochastic differential equation are stud-
ied
dxt =
Xm
k=1
Ak
t xtdwk(t) + Btxtdt
where Ak
t , Bt are (deterministic) continuous matrix-valued functions of t and w1(t), · · ·,
wm(t) are m independent standard Brownian motions. Conditions are given such that the
solution is positive if the initial condition is positive. The equation the most probable path
must satisfy is also derived and applied to a mathematical finance problem.

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9. GLOBAL STABILITY OF AN SIRS EPIDEMIC MODEL WITH DELAYS

靳祯; 马知恩; 韩茂安

数学物理学报(英文版) DOI: 10.1016/S0252-9602(06)60051-9

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10. CLASSIFICATION OF POSITIVE SOLUTIONS FOR NONLINEAR DIFFERENTIAL AND INTEGRAL SYSTEMS WITH CRITICAL EXPONENTS

Wenxiong Chen, Congming Li

数学物理学报(英文版) 2009, 29 (4): 949-960. DOI: 10.1016/S0252-9602(09)60079-5

摘要（1098）

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We classify all positive solutions for the following integral system:

u_i(x) =∫_Rn1/ |x − y|^n−α f_i(u(y))dy, x ∈ Rⁿ, i = 1, · · · , m,

0 < α < n, and u(x) = (u₁(x), u₂(x), · · · , u_m(x)).

Here f_i(u), 1 ≤ i ≤ m, are real-valued functions of homogeneous degree n+α/ n−α and are monotone nondecreasing with respect to all the independent variables u₁, u2, · · ·, u_m. In the special case n ≥ 3 and α = 2, we show that the above system is equivalent to the following elliptic PDE system:

−△u_i(x) = f_i(u(x)), x ∈ Rⁿ, i = 1, · · · , m,

and u(x) = (u₁(x), u₂(x), · · · , u_m(x)).

This system is closely related to the stationary Schr¨odinger system with critical exponents for Bose-Einstein condensate.

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11. ASYMPTOTIC BEHAVIOR OF SOLUTIONS TOWARD THE SUPERPOSITION OF CONTACT DISCONTINUITY AND SHOCK WAVE FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY

Hakho Hong, Feimin Huang

数学物理学报(英文版) 2012, 32 (1): 389-412. DOI: 10.1016/S0252-9602(12)60025-3

摘要（689）

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A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated. The asymptotic behavior of solutions toward the superposition of contact discontinuity and shock wave is established under some smallness conditions. To do this, we first construct a new viscous contact wave such that the momentum equation is satisfied exactly and then determine the shift of the viscous shock wave. By using them
together with an inequality concerning the heat kernel in the half space, we obtain the desired a priori estimates. The proof is based on the elementary energy method by the anti-derivative argument.

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12. EIGENFUNCTION EXPANSION FOR STURM-LIOUVILLE PROBLEMS WITH TRANSMISSION CONDITIONS AT ONE INTERIOR POINT

Oktay Sh. MUKHTAROV, Kadriye AYDEMIR

数学物理学报(英文版) 2015, 35 (3): 639-649. DOI: 10.1016/S0252-9602(15)30010-2

摘要（84）

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The purpose of this article is to extend some spectral properties of regular Sturm-Liouville problems to the special type discontinuous boundary-value problem, which consists of a Sturm-Liouville equation together with eigenparameter-dependent boundary conditions and two supplementary transmission conditions. We construct the resolvent operator and Green's function and prove theorems about expansions in terms of eigenfunctions in modified Hilbert space L₂[a, b].

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13. PROJECTIVELY FLAT MATSUMOTO METRIC AND ITS APPROXIMATION

李本伶

数学物理学报(英文版) DOI: 10.1016/S0252-9602(07)60075-7

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14. A SHORT NOTE ABOUT EXPOSED POINTS IN REAL BANACH SPACES

Antonio Aizpuru; Francisco J Garc

数学物理学报(英文版) DOI: 10.1016/S0252-9602(08)60080-6

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15. INTERIOR ESTIMATES IN MORREY SPACES FOR SOLUTIONS OF ELLIPTIC EQUATIONS AND WEIGHTED BOUNDEDNESS FOR COMMUTATORS OF SINGULAR INTEGRAL OPERATORS

刘岚喆

数学物理学报(英文版) 2005, 25 (1): 89-94.

摘要（812）

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It is proved that, for the nondivergence elliptic equations $\sum_{i,j=1}^n$

$a_{ij}u_{x_ix_j}=f$, if $f$ belongs to the generalized Morrey spaces

$L^{p,\varphi}(\omega)$, then $u_{x_ix_j}\in L^{p, \varphi}(\omega)$, where $u$ is the $W^{2,p}$-solution of the equations. In order to obtain this, the author first establish

the weighted boundedness for the commutators of some singular integral operators on $L^{p,\varphi}(\omega)$. \noindent\ke{\bf Key words}{\rm Nondivergence elliptic equation, generalized Morrey space, commutator of singular integral operator, $A_p$ weight}

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16. GLOBAL ATTRACTOR OF NONLINEAR STRAIN
WAVES IN ELASTIC WAVEGUIDES

戴正德, 郭柏灵

数学物理学报(英文版) 2000, 20 (3): 322-334.

摘要（668）

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The initial-boundary value problem of the propagation of nonlinear longitudinal
elastic waves in an initially strained rod is considered. The rod is assumed to interact
with the surrouding elastic and viscous external medium. The long time behavior of solutions
are derived and global attractors in E1 space is obtained.

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17. ATTRACTORS FOR FULLY DISCRETE FINITE DIFFERENCE SCHEME OF DISSIPATIVE ZAKHAROV EQUATIONS

张法勇, 郭柏灵

数学物理学报(英文版) 2012, 32 (6): 2431-2452. DOI: 10.1016/S0252-9602(12)60190-8

摘要（447）

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A fully discrete finite difference scheme for dissipative Zakharov equations is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions, the stability of the difference scheme and the error bounds of optimal order of the difference solutions are obtained in L² ×H¹ ×H² over a finite time interval (0, T]. Finally, the existence of a global attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.

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18. THE INTERIOR LAYER PHENOMENA FOR A CLASS OF SINGULARLY PERTURBED DELAY-DIFFERENTIAL EQUATIONS

汪娜, 倪明康

数学物理学报(英文版) 2013, 33 (2): 532-542. DOI: 10.1016/S0252-9602(13)60017-X

摘要（611）

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In this article, we study a kind of vector singularly perturbed delay-differential equation. Using boundary layer function method and geometric analysis skill, the asymptotic expression of the system is constructed and the uniform validity of asymptotic solution is also proved.

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19. PARAMETER IDENTIFICATION IN FRACTIONAL DIFFERENTIAL EQUATIONS

李景, 郭柏灵

数学物理学报(英文版) 2013, 33 (3): 855-864. DOI: 10.1016/S0252-9602(13)60045-4

摘要（258）

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This article investigates the fractional derivative order identification, the coef-ficient identification, and the source identification in the fractional diffusion problems. If 1 < < 2, we prove the unique determination of the fractional derivative order and the dif-fusion coefficient p(x) by R t0 u(0, s)ds, 0 < t < T for one-dimensional fractional diffusion-wave equations. Besides, if 0 < < 1, we show the unique determination of the source term f(x, y) by U(0, 0, t), 0 < t < T for two-dimensional fractional diffusion equations. Here, denotes the fractional derivative order over t.

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20. THE STABILITY OF STATIONARY SOLUTION FOR OUTFLOW PROBLEM ON THE NAVIER-STOKES-POISSON SYSTEM

蒋咪娜, 赖素华, 尹海燕, 朱长江

数学物理学报(英文版) 2016, 36 (4): 1098-1116. DOI: 10.1016/S0252-9602(16)30058-3

摘要（80）

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In this article, we are concerned with the stability of stationary solution for outflow problem on the Navier-Stokes-Poisson system. We obtain the unique existence and the asymptotic stability of stationary solution. Moreover, the convergence rate of solution towards stationary solution is obtained. Precisely, if an initial perturbation decays with the algebraic or the exponential rate in space, the solution converges to the corresponding stationary solution as time tends to infinity with the algebraic or the exponential rate in time. The proof is based on the weighted energy method by taking into account the effect of the self-consistent electric field on the viscous compressible fluid.

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