Modified Boussinesq方程的变量分离

利用和三阶特征值问题相联系的零曲率方程表示理论，本文给出ＭｏｄｉｆｉｅｄＢｏｕｓｓｉｎｅｓｑ方程在显式约束和高阶约束下的两种分解，ＭｏｄｉｆｉｅｄＢｏｕｓｓｉｎｅｅｓｑ方程对ｘ和ｔ的依赖被分解为两个可交换的ｘ－和ｔ－有限维可积的Ｈａｍｉｌｔｏｎ系统．这种分解提供了类似于变量分离的求解方法，通过解两个可交换的有限维可积系统可得到ＭｏｄｉｆｉｅｄＢｏｕｓｓｉｎｅｓｑ方程的某些解．     

解高维广义对称正则长波方程的Fourier谱方法

１引言对称正则长波方程（ＳＲＬＷＥ）是正则化长波方程（ＲＬＷＥ）的一种对称叙述［１］用于描述弱非线性作用下空间变换的离子声波传播．［１］得到了方程组（１．１）的双曲正割平方孤立波解、四个不变量和数值结果、明显地,从（１．１）中消去ρ,得到一类正则长波方程（ＲＬＷＥ）代替（１．２）中第三项、第四项对ｔ的导数为对ｘ的导数,得到Ｂｏｕｓｓｉｎｅｓｑ方程．［２］对一类广义对称正则长波方程组提出了谱方法,证明了古典光滑解的存在性和唯一性,建立了近似解的收敛性和误差估计。［３］研究了高维对称正则长波方程整体…     

一类广义Boussinesq方程解的Blowup

该文利用Ｆｏｕｒｉｅｒ变换方法研究一类广义Ｂｏｕｓｓｉｎｅｓｑ方程ｕｔｔ－ｕｘｘ＝ｂｕｘｘｘ＋ａ（ｕｐ）ｘｘ＋ｃｕｑ的初边值问题的局部解的存在性与整体解的不存在性．其中ｂ＞０，ａ，ｃ为任意实数，ｐ≥１，ｑ≥１为整数．我们得到了上述问题的局部解存在和解在有限时刻ｂｌｏｗｕｐ的一些充分条件并且给出了几个具体实例．     

Boussinesq型方程的周期边界问题与初值问题的解的存在性

本文研究“坏的Ｂｏｕｓｓｉｎｅｓｑ型方程ｕｔｔ－ｂｕｘｘｘ＝σ（ｕ）ｘｘ的周期边界问题与初值问题的解的存在性问题，其中ｂ〉０为常数，证明了在相当宽松的条件下，上述问题存在局部广义解。     

一类非线性发展方程的精确孤波解

本文首先求出了非线性常微分方程ｕ″（ξ）＋ｍｕ２（ξ）＋ｎｕ３（ξ）＋ｐｕ（ξ）＝ｃ（Ⅰ）和ｕ″（ξ）＋ｒｕ′（ξ）＋ｍｕ２（ξ）＋ｎｕ３（ξ）＋ｐｕ（ξ）＝ｃ（Ⅱ）的显式精确解．进而求出了组合ＢＢＭ方程、Ｂｕｒｇｅｒｓ方程与组合ＢＢＭ方程混合型的钟状孤波解和扭状孤波解，同时还求出了广义Ｂｏｕｓｓｉｎｅｓｑ方程和广义ＫＰ方程的钟状和扭状孤波解．文中指出了其行波解可化为（Ⅰ）的发展方程既有钟状又有扭状孤波解，而其行波解可化为（Ⅱ）的发展方程没有钟状孤波解．     

弱阻尼非线性Scdrodinger－Boussinesq方程整体吸引子的有限维性质

弱阻尼非线性Ｓｃｄｒｏｄｉｎｇｅｒ－Ｂｏｕｓｓｉｎｅｓｑ方程整体吸引子的有限维性质郭柏灵，陈风新ＦｉｎｉｔｅＤｉｍｅｎｓｉｏｎａｌＢｅｈａｖｉｏｒｏｆＧｌｏｂａｌＡｔｔｒａｃｔｏｒｓＦｏｒｗｅａｋｌｙＤａｍｐｅｄＮｏｎｌｉｎｅａｒＳｃｈｒｏｄｉｎｇｅ...     

环形空腔内自然对流问题的的Galerkin方法

本文讨论了环形空腔内自然对流问题所满足的Ｂｏｕｓｓｉｎｅｓｑ方程组－关于涡度ζ、流函数ψ及温度θ的椭圆－抛物非线性耦合方程组用Ｇａｌｅｒｋｉｎ方法对其进行了数值分析，得到了Ｇａｌｅｒｋｉｎ逼近（含半离散和全离散）的最优先验误差估计。     

有限变极性弹性介质的各型动力学方程组

本文从Ｄｌｕｚｅｗｓｋｉ提出的以欧拉角为角坐标的建议和推导出的Ｃａｕｃｈｙ型动力学方程组出发，又引进若干有关变形几何学和动力学的新定义并推导出有限变形极性弹性介质的Ｂｏｕｓｓｉｎｅｓｑ型、Ｋｉｒｃｈｈｏｆｆ型、Ｓｉｇｎｏｒｉｎｉ型     

On the Suitable Weak Solutions to the Boussinesq Equations in a Bounded Domain

ＯｎｔｈｅＳｕｉｔａｂｌｅＷｅａｋＳｏｌｕｔｉｏｎｓｔｏｔｈｅＢｏｕｓｓｉｎｅｓｑＥｑｕａｔｉｏｎｓｉｎａＢｏｕｎｄｅｄＤｏｍａｉｎＧｕｏＢｏｌｉｎｇ（郭柏灵）ＹｕａｎＧｕａｎｇｗｅｉ（袁光伟）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＰｈｙｓｉｃｓａｎ...     

The Initial-Boundary Value Problem for the Boussinesq Equations

ＴｈｅＩｎｉｔｉａｌ－ＢｏｕｎｄａｒｙＶａｌｕｅＰｒｏｂｌｅｍｆｏｒｔｈｅＢｏｕｓｓｉｎｅｓｑＥｑｕａｔｉｏｎｓｗｉｔｈＤａｔａｉｎＬ￣ＰＧｕｏＢｏｌｉｎｇ（郭柏灵），ＹｕａｎＧｕａｎｇｗｅｉ（袁光伟）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＰｈｙｓｉ...     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].