解二维抛物型方程的高精度差分格式

本文构造了一个解二维抛物型方程的高精度三层显式差分格式,其稳定性条件为r=△t/△x2=△t/△y2≤1/4,截断误差为O(△t2+△x4).     

四维抛物型方程的高精度分支稳定的显式差分格式

对四维抛物型方程构造了一个高精度显格式,格式的稳定性条件为r=Δt/Δx2=△t/Δy2=△t/△z2=Δt/Δw2<1/2,截断误差阶达到O(Δt2 Δx4),通过数值实验,表明本文理论分析的正确性和文中格式较同类格式的优越性.     

Biharmonic equations with asymptotically linear nonlinearities

This article considers the equation △2u = f(x, u)with boundary conditions either u|(a)Ω = (a)u/(a)n|(a)Ω = 0 or u|(a)Ω = △u|(a)Ω = 0, where f(x,t) is asymptotically linear with respect to t at infinity, and Ω is a smooth bounded domain in RN, N ＞ 4. By a variant version of Mountain Pass Theorem, it is proved that the above problems have a nontrivial solution under suitable assumptions of f(x, t).     

ON THE EQUATION □φ=｜↓△φ｜^2 IN FOUR SPACE DIMENSIONS

This paper considers the following Cauchy problem for semilinear wave equations in n space dimensions □φ=F(δφ),φ(0,x)=f(x),δtφ(0,x)=g(x),whte □=δt^2-△ is the wave operator,F is quadratic in δεφ with δ=(δt,δx1,…,δxn).The minimal value of s is determined such that the above Cauchy problem is locally wellposed in H^s.It turns out that for the general equation s must satisfy s&gt;max(n/2,n+5/4).This is due to Ponce and Sideris (when n=3)and Tataru (when n≥5).The purpose of this paper is to supplement with a proof in the case n=2,4.     

高阶Schr(o..)dinger方程的一族恒稳差分格式

A family of three-layer implicit difference schemes of high accuracy with two parameters for solving high order Schroedinger type equation au/at = i(-1)^m a^2mu/ax^2m are constructed(where i = √-1,m is positive integers). In the special case α =1/2,β = 0,we obtain a two-layer difference scheme. These schemes are proved to be absolutely stable for arbitrarily chosen non-negative parameters, and the order of the truncation error is O((△t)^2 (△x)^4). They are shown by numerical examples to be effective, and practice consistant with theoretical analysis.     

三维抛物型方程的一族两层高精度显式格式

A class of two-level high-order accuracy explicit difference scheme for solving 3-D parabolic P.D.Eis constructed.Its truncation error is (△t^2 △x^4)and the stability condition is r=△t/△x^2=△t/△y^2=△t/△z^2≤1/6.     

THE EXISTENCE OF GLOBAL SOLUTION AND THE BLOWUP PROBLEM FOR SOME p-LAPLACE HEAT EQUATIONS

This article consider, for the following heat equation ut/|x|s-△pu=uq,(x,t)∈Ω×(0,T), u(x,t)=0,(x,t)∈(?)Ω×(0,T), u(x,0)=u0(x),u0(x)≥0,u0(x)(?)0 the existence of global solution under some conditions and give two sufficient conditions for the blow up of local solution in finite time, whereΩis a smooth bounded domain in RN(N>p),0∈Ω,△pu=div(|▽u|p-2▽u),0≤s≤2,p≥2,p-1相似文献   

Existence Results for a Class of Semilinear Elliptic Systems

In this paper, we study the existence of nontrivial solutions for the problem
{-△u=f（x,u,v）＋h1（x）in Ω
-△v=g（x,u,v）＋h2（x）inΩ
u=v=0 onδΩ
where Ω is bounded domain in R^N and h1,h2 ∈ L^2 （Ω）. The existence result is obtained by using the Leray-Schauder degree under the following condition on the nonlinearities f and g：
{lim s,｜t｜→＋∞f（x,s,t）/s=lim ｜s｜,t→＋∞g（x,s,t）/t=λ＋1 uniformly on Ω,
lim -s,｜t｜→＋∞f（x,s,t）/s=lim ｜s｜,-t→＋∞g（x,s,t）/t=λ-,uniformly on Ω,
where λ＋,λ-∈（0）∪σ（-△）,σ（-△）denote the spectrum of -△. The cases （i） where λ＋ = λ_ and （ii） where λ＋≠λ_ such that the closed interval with endpoints λ＋,λ_ contains at most one simple eigenvatue of -△ are considered.     

高阶抛物型方程的一族高精度恒稳差分格式

A family of three-layer implicit difference Schemes of high accuracy with two parameters for solving high order parabolic equationδu/δt=(-1)^m 1δ^2mu/δx^2m(where m is positive integers) are constructed. In the special case α=1/2, β=0, We obtain a two-layer difference scheme. These schemes are proved to be absolutely stable for arbiratily chosen non-negative parameters, And the order of the truncation error is O((△t)^2 (△x)^6). They are shown by numerical examples to be effective, and practice consistant with theoretical analysis.     

人口问题中广义三维GINZBURG-LANDAU模型方程

本文讨论三维广义Ginzburg-Landau模型方程的初边值问题ut=-a1↓△^4u a2↓△^2u ↓△^2g(u) G(u),σu/σv=0,σ△u/σv=0,u(x,0)=u0(x)解的整体存在性、唯一性、渐近性质和爆破。     

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.     

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 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].