具有时间依赖记忆核的非经典扩散方程的吸引子

该文在时间依赖空间H₀¹(Ω)×L_μt²(R⁺;H₀¹(Ω))中研究了具有时间依赖记忆核的非经典扩散方程解的长时间动力学行为.在新的理论框架下,利用积分估计方法以及分解技术得到了解的适定性,进而证明了时间依赖全局吸引子的存在性与正则性.     

Cahn-Hilliard-Brinkman系统的全局吸引子

研究了具有一般非线性条件的Cahn-Hilliard-Brinkman系统的弱解的适定性,分析了解的渐近性态,并通过渐近能量估计得到在H^s(Ω)(s=1,2,3,4)中全局吸引子的存在性.     

一类推广的BBM方程的强吸引子

主要研究了推广的Benjamin-Bona-Mahony（BBM）方程的解的渐近行为,通过证明半群的渐近紧性证明了方程在H)_per²（Ω）中全局吸引子的存在性.     

无热耗散d维热带气候模型的小初值整体解

本文研究小初值情况下无热耗散d(d≥2)维热带气候模型的整体适定性问题,文中考虑的模型在速度的正压模和第一斜压模方程上分别具有分数阶耗散Λ^2α u的Λ^2β v.当0≤α<1,■≤β≤1且α+β≥1时,在小初值的假设下,我们建立了整体解的存在性和唯一性.     

关于特征情形的部分亚椭圆定理及其应用

<正> 边值问题的适定性和其解的正则性有紧密的联系.在研究边值问题解到边界的正则性时,Hrmander([2])的部分亚椭圆定理起着十分重要的作用.在研究蜕缩椭圆、双曲和混合型算子的边值问题时,提出了特征情形下的部分亚椭圆定理的问题.考虑Ω=R~(n-1)X(0,1)上的一阶算子方程.     

Laplace算子特征值和的精细下界

该文研究了Rⁿ中Laplace算子在有界域Ω上的Dirichlet特征值和的下界.众所周知:第k个Dirichlet特征值λ_k(Ω)服从Weyl渐近公式,即λ_k(Ω)～4π²/[w_nV(Ω)]^2/nk^2/n当k→∞时,其中w_n和V(Ω)分别为是Rⁿ中n维单位球的体积和Ω的体积.根据上述公式,Pólya猜测λ_k(Ω)≥4π²/[w_nV(Ω)]^2/nk^2/n,?k∈N.这就是著名的Pólya猜想.对这一问题的研究由来已久,已有很多的工作.特别是,近几十年来最显著的成就之一是由Berezin^[4],以及李伟光和丘成桐^[3]分别独立取得的.他们部分解决了Pólya猜想,只是多了一个因子n/(n+2).后来,Melas^[7]改进...     

Smarandache双阶乘对偶函数的三次均值及加权均值

利用初等方法研究了Smarandache双阶乘对偶函数S^(**)(n)的三次均值及其加权均值,给出了∑_(n≤x)(S(**)(n)的三次均值及其加权均值,给出了∑_(n≤x)(S^(**)(n))(**)(n))³,∑_(n≤x)n3,∑_(n≤x)n^k(Sk(S^(**)(n))(**)(n))³及∑(n≤x(S3及∑(n≤x(S^(**)(n)(**)(n)³/n3/n^k)的渐近公式,得到了Sk)的渐近公式,得到了S^(**)(n)新的分布性质,补充了有关文献的结论.     

次临界Choquard方程的多解

该文考虑次临界Choquard方程■(0.1)多解的存在性,其中N> 3,λ是正实参数,p_ε=2_μ^*-ε,ε> 0,0 <μμ^*=(2N-μ)/(N-2)是Hardy-Littlewood-Sobolev不等式意义下的临界指数.假定Ω:=int V^-1(0)是R^N中非空带光滑边界的有界区域,利用Lusternik-Schnirelman定理,该文证明了当λ足够大及ε充分小时,方程(0.1)至少有cat_Ω(Ω)个正解.     

一类具有局部化源和吸收项的抛物系统解的整体存在与爆破

在齐次Dirichlet边界条件研究如下抛物系统其中x_0(t):R⁺→(0,a)是Holder连续函数;常数0≤α,β<1,p_1,p_2,q_1,q_2,k_1,k_2>0.利用正则化方法,在一定的假设条件下证明了经典解的存在性.接着利用比较原理证明了该系统正解的整体存在性和爆破性.最后给出了爆破解的精确爆破速率和爆破模式.     

非线性Kirchhoff型波动方程解的真空隔离（英文）

本文研究初边值问题其中Ω是Rⁿ中的有界区域,A=-△是定义在A=-△上的Laplace算子.利用位势井方法得到了解的存在性定理,并且证明了当e∈（0,d）时,以E（0）∈(0,e]为初始能量的所有解只能位于空间D(A^1/2)中小球的外部和大球的内部,其中,C_*是空间D(A^1/2)到L^p+1（Ω）的嵌入常数.     

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

正~~     

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].