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Quadrature-free spline method for two-dimensional Navier-Stokes equation

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Applied math.matics(A Journal of Chinese Universities) 2008年第1期23卷 31-42页

作者： HU Xian-liang HAN Dan-fu dept. of math. Zhejiang Univ. Hangzhou 310027 China.

In this paper, a quadrature-free scheme of spline method for two-dimensional Navier- Stokes equation is derived, which can dramatically improve the efficiency of spline method for fluid problems proposed by Lai and Wenston（2004）. Additionally, the explicit formulation for boundary condition with up to second order derivatives is presented. The numerical simulations on several benchmark problems show that the scheme is very efficient.

关键词： quadrature-free spline method Navier-Stokes equation.

ON RANDOM TOPOLOGICAL DEGREE AND SOME RANDOM FIXED POINT THEOREMS

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Acta math.matica Scientia 1993年第4期13卷 391-398页

作者：李国桢陈玉清 dept. of math. Jiangxi Norm. Univ. Nanchang 330027 China dept. of math. Fordham Univ. NY 10458 USA

In this paper we first introduce random topological degree, and then we use random topological degree to prove some new random fixed point theorems which are the randomization of the well-known classical theorems of Altman and Krasnosalskii etc. We also proved some other new random fixed point theorems. We first introduce topological degree method to random fixed posnt theory.

关键词：随机拓扑度随机不动点随机化

UNIQUENESS OF THE MILD SOLUTION OF SEMILINEAR STOCHASTIC EVOLUTION EQUATION IN HILBERT SPACE

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Acta math.matica Scientia 1993年第4期13卷 384-390页

作者：许明浩胡则成 dept. of math. Wuhan Univ. Wuhan 430072 China dept. of math. Wuhan Univ. of Tech. Wuhan 430070 China

In this paper, we will consider following initial value problem of semilinear stochastic evolution equation in Hilbert Space: [GRAPHICS] where W(t) is a wiener process in H, H and Y are two real separable Hilbert Spaces, A is an infinitesimal generator of a strongly continuous semigroup s(t) on Y, f(t, y): [0, T] x Y --> Y, and G(t, y): [0, T] X Y --> L(H, Y), y0: OMEGA --> Y is a ramdom variable of square integrable. We apply theory of the semigroup and obtain two conclusions of uniqueness of the mild solution of (1) which include the corresponding results in [4].

关键词： MILD UNIQUENESS OF THE MILD SOLUTION OF SEMILINEAR STOCHASTIC EVOLUTION EQUATION IN HILBERT SPACE

FINITE SPEED OF PROPAGATION OF SOLUTIONS FOR SOME QUASILINEAR HIGHER ORDER PARABOLIC EQUATIONS WITH DOUBLY STRONG DEGENERATION

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Acta math.matica Scientia 1991年第2期11卷 164-174页

作者：尹景学 dept. of math. Jilin Univ. Changchun China

Under some conditions, one seows that the generalized solutions of the first boundary value problem for the equation [GRAPHICS] have the property of finite speed of propagation.

关键词： FINITE SPEED OF PROPAGATION OF SOLUTIONS FOR SOME QUASILINEAR HIGHER ORDER PARABOLIC EQUATIONS WITH DOUBLY STRONG DEGENERATION QPE

INVARIANT MEASURES FOR THE SINGLEPARAMETER TRANSFORMATION GROUP WITH COMPACT ORBITS ON BANACH SPACES

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Acta math.matica Scientia 1988年第1期8卷 79-84页

作者：刘勇 dept. of math. Wuhan University China

§1. Introduction In this paper we concern an invariant probability measure with respect to the single-parameter transformation group (?)= {S: t∈(?)} on some Banach space B. In some cases, the group (?) is determined... 详细信息

关键词： Th INVARIANT MEASURES FOR THE SINGLEPARAMETER TRANSFORMATION GROUP WITH COMPACT ORBITS ON BANACH SPACES

Remarks on homoclinic solutions for semilinear fourth-order ordinary differential equations without periodicity

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Applied math.matics(A Journal of Chinese Universities) 2009年第1期24卷 49-55页

作者： LI Cheng-yue dept. of math. Central Univ. for Nationalities Beijing 100081 China

This paper mainly discusses the existence of nontrivial homoclinic solutions for nonperiodic semilinear fourth-order ordinary differential equation u^（4）＋pu″＋a（x）u-b（x）u^2=c（x）u^3=3arising in the study of p... 详细信息

关键词： homoclinic solution Mountain Pass Lemma Extended Fisher-Kolmogorov (EFK) equation Swift-Hohenberg (SH) equation

A math.MATICAL ANALYSIS FOR A DIFFUSIVE EPIDEMIC MODEL WITH CRISS-CROSS DYNAMICS

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Applied math.matics(A Journal of Chinese Universities) 1999年第4期14卷 389-400页

作者： Li Zhengyuan\ Tao Jiyuan\ Ye Qixiao dept. of math. Peking Univ. Beijing dept. of Appl. math. Beijing Institute of Technology Beijing

In this paper, an initial boundary value problem with homogeneous Neumann boundary condition is studied for a reaction\|diffusion system which models the spread of infectious diseases within two population groups by means of self and criss\|cross infection mechanism. Existence, uniqueness and boundedness of the nonnegative global solution ( u\-1,u\-2,u\-3,u\-4) , existence of the limit of the solution as t→+∞ ,namely,( u\-1,u\-2,u\-3,u\-4)→(u\+*\-1,0,u\+*\-3,0), are proved.

关键词： Upperandlowersolutions boundedness Liapunovfunctionalmethod exponentialdelayestimates

OPTIMAL QUADRATURE OF THE SOBOLEV CLASS W_1~r(R) DEFINED ON WHOLE REAL AXIS

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Acta math.matica Scientia 1996年第1期16卷 72-80页

作者：房艮孙刘永平 dept. of math. Beijing Normal Univ. Beijing 100875 China

In this paper,we study the optimal quadrature problem with Hermite-Birkhoff type,on the Sobolev class(R)defined on whole red axis,and we give an optimal algorithm and determite its optimal error.

关键词： quadrature formula,optimal algorithm optimal error.

INTERACTION OF STRONG AND WEAK SINGULARITIES FOR HYPERBOLIC SYSTEM OF CONSERVATION LAWS IN MULTIDIMENSIONAL SPACE

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Acta math.matica Scientia 1990年第3期10卷 298-302页

作者：陈恕行 dept. of math. Fudan University Shanghai China

In this paper we study the interaction of strong and weak singularities for hyperbolic system of conservation laws in multidimensional space. Under the assumption of transversal intersect of the shock front with the b... 详细信息

关键词： INTERACTION OF STRONG AND WEAK SINGULARITIES FOR HYPERBOLIC SYSTEM OF CONSERVATION LAWS IN MULTIDIMENSIONAL SPACE