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TOEPLITZ C-ALGEBRA OVER THE L-SHAPED DOMAIN IN C^m

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Chinese Annals of mathematics,Series B 1996年第3期17卷 325-334页

作者： XU SHENGZHI CHEN XIAOMAN YAN SHAOZONG(institute of mathematics,{2., Shanghai 2.0433, china) institute of mathematics Fudan University Shanghai 200433 China

The authors investigate the Toeplitz C-algebra over the L-shaped domain in Cn by thegroupoid approach, and successfully parameterise the unit space of the groupoid associated tothe Toeplitz C-algebra.

关键词： L-shaped domain Toeplitz C-algebra Parameterization

Harmonic maps with potential from complete manifolds

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Chinese Science Bulletin 1998年第21期43卷 1780-1786页

作者： CHEN Qun mathematics Department, Central china Normal {2., Wuhan 430079, china institute of mathematics, fudan university, Shanghai 2.0433, china mathematics Department Central China Normal University Wuhan China institute of mathematics Fudan University Shanghai China

Harmonic maps with potential from complete manifolds are considered. This is a new kind of maps more general than the usual harmonic maps relating to many interesting problems such as equilibrium system of ferromagnetic spin chain and Neumann motion. Aiming at the general properties, the author derives basic gradient estimates and then Liouville type results for these maps, which are interesting in constrast to those of the usual harmonic maps for the presence of potentials.

关键词： harmonic maps potential ferromagnetic chain gradient estimate.

Numerical Computation of High Dimensional Solitons Via Darboux Transformation

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Communications in Nonlinear Science and Numerical Simulation 1997年第4期2卷 248-252页

作者： Zixiang ZHOU (institute of mathematics,{2. university,Shanghai 2.0 0 433,china) E- mail:zxzhou@*** institute of mathematics Fudan University Shanghai 200433 China

Darboux transformation gives explicit soliton solutionsof nonlinear partial differential equations. Using numerical computation in each step of constructing Darboux transformation,one can get the graphs of the solitons ***(n 3) , this method greatly increases the speed and deduces the memory usage of computation comparing to the software for algebraic computation. A technical problem concerning floating overflow is discussed.

关键词： Darboux transformation numerical computation

On the Neighborhood in Stabilizing Period-T Orbits for Chaotic m Degree Polynomial Dynamical System

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Communications in Nonlinear Science and Numerical Simulation 1998年第4期3卷 242-247页

作者： Enguo GU Jiong RUAN and Zhenxun HUANG (institute of mathematics,{2., Shanghai 2.0433,china) institute of mathematics Fudan University Shanghai 200433 China

In this paper, a problem of stabilizing a period-T orbit in discrete Chaotic m degree polynomial dynamical systems is studied. The aim is to present a new method for determining the neighborhood of a period-T point in which the system remains stable when subjected to a linear feedback control. A theorem on the existence of neighborhood is rigorously proved using idea from functional analysis and polar coordinate *** ways of implementing the obtained theorem in the Henon map are proposed. Thevalidity of this method is shown by numerical simulation.

关键词： neighborhood of period-T orbit controlling chaotic discrete system gain matrix

SOME REMARKS ON THE NULL CONDITION FOR NONLINEAR ELASTODYNAMIC SYSTEM

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Chinese Annals of mathematics,Series B 2002年第3期23卷 311-316页

作者： XIN JIE institute of mathematics, Laboratory of mathematics for Nonlinear sciences, Pudan university, Shanghai 2.0433, china. institute of mathematics Laboratory of Mathematics for Nonlinear Sciences Fudan University Shanghai 200433 China

The author derives the same null condition as in [1] for the nonlinear elastodynamic system in a simpler way and proves the equivalence of the null conditions introduced in [1] and [7] respectively.

关键词： Null condition Stored energy function Elastodynamic system

Regularity of harmonic maps with the potential

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Science china mathematics 2006年第5期49卷 599-610页

作者： CHU Yuming & LIU Xiangao Department of mathematics, Huzhou Teachers College, Huzhou 313000, china {2. of mathematics, fudan university, Shanghai 2.0433, china Department of mathematics Huzhou Teachers College Huzhou 313000 China institute of mathematics Fudan University Shanghai 200433 China

The aim of this work is to prove the partial regularity of the harmonic maps with potential. The main difficulty caused by the potential is how to find the equation satisfied by the scaling function. Under the assumption on the potential we can obtain the equation, however, for a general potential, even if it is smooth, the partial regularity is still open.

关键词： harmonic map, partial regularity, potential.

FORMATION OF SINGULARITIES FOR A KIND OF QUASILINEAR NON-STRICTLY HYPERBOLIC SYSTEM

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Chinese Annals of mathematics,Series B 2002年第4期23卷 439-454页

作者： WANG LIBINinstitute of mathematics,{2., Shanghai 2.0433, china. institute of mathematics Fudan University Shanghai 200433 China

The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.

关键词： Formation of singularity Quasilinear non-strictly hyperbolic system Weak linear degeneracy

ON SOME CONSTANTS OF QUASICONFORMAL DEFORMATION AND ZYGMUND CLASS

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Chinese Annals of mathematics,Series B 1995年第3期16卷 325-330页

作者： CHEN JIXIU WEI HANBAI(institute of mathematics,{2., Shanghai 2.0433, china.) fudan UNIV INST MATHSHANGHAI 200433PEOPLES R CHINA

A real-valued function f(x)on belongs to Zygmund class if its Zygmund norm It is proved that when f ∈, there exists an extension F(z)of f to H = {Imz > 0} such that It is also proved that if f(0)=f(1)= 0,then

关键词： Quasiconformal deformation Zygmund class Beurling-Ahlfors extension.

A HYPERBOLIC SYSTEM OF CONSERVATION LAWS FOR FLUID FLOWS THROUGH COMPLIANT AXISYMMETRIC VESSELS

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Acta Mathematica Scientia 2010年第2期30卷 391-427页

作者： Gui-Qiang G.Chen school of mathematical sciences,fudan {2.,Shanghai 2.0433,china mathematical institute,{2. of Oxford,2.-2. St Giles,Oxford,OX1 3LB,UK Department of mathematics,Northwestern {2.,Evanston,IL 602.8-2.30,USA Weihua Ruan Department of mathematics,Computer Science and Statistics,Purdue {2. Calumet,Hammond,IN 4632.-2.94,USA [a] school of mathematical sciences Fudan University Shanghai 200433 China [b] Mathematical Institute University of Oxford 24-29 St Giles Oxford OX1 3LB UK [c] Department of Mathematics Northwestern University Evanston IL 60208-2730 USA [d] Department of Mathematics Computer Science Statistics Purdue University Calumet Hammond IN 46323-2094 USA

We are concerned with the derivation and analysis of one-dimensional hyperbolic systems of conservation laws modelling fluid flows such as the blood flow through compliant axisyminetric vessels. Early models derived are nonconservative and/or nonho- mogeneous with measure source terms, which are endowed with infinitely many Riemann solutions for some Riemann data. In this paper, we derive a one-dimensional hyperbolic system that is conservative and homogeneous. Moreover, there exists a unique global Riemann solution for the Riemann problem for two vessels with arbitrarily large Riemann data, under a natural stability entropy criterion. The Riemann solutions may consist of four waves for some cases. The system can also be written as a 3 × 3 system for which strict hyperbolicity fails and the standing waves can be regarded as the contact discontinuities corresponding to the second family with zero eigenvalue.

关键词： conservation laws hyperbolic system fluid flow blood flow vessel hyper-bolicity Riemann problem Riemann solution wave curve shock wave rarefaction wave standing wave stability