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Global Existence of Classical Solutions for Some Oldroyd-B Model via the Incompressible Limit

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Chinese Annals of mathematics,Series B 2006年第5期27卷 565-580页

作者： Zhen LEI School of Mathematical sciences, fudan university, shanghai 200433, china School of mathematics and Statistics, Northeast Normal university, Changchun 130024, china. School of Mathematical sciences Fudan University Shanghai 200433 China School of mathematics and Statistics Northeast Normal University Changchun 130024 China

In this paper, we prove local and global existence of classical solutions for a system of equations concerning an incompressible viscoelastic fluid of Oldroyd-B type via the incompressible limit when the initial data ... 详细信息

关键词： Incompressible limit Global existence Oldroyd model

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, fudan university, shanghai 200433, 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

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, fudan university, shanghai 200433,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

TENSOR PRODUCTS OF JACOBSON RADICALS IN NEST ALGEBRAS

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Chinese Annals of mathematics,Series B 2003年第3期24卷 323-330页

作者： DONG ZHE Departinent of mathematics, Zhejiang university, Hangzhou 310027, china. Institute of mathematics, fudan university, shanghai 200433, china. Department of mathematics Zhejiang University Hangzhou 310027 China Institute of mathematics Fudan University Shanghai 200433 China

This paper studies the tensor product RN RM of Jacobson radicals in nest algebras, and obtains that RN RM = {T∈B(H1 H2) : T(N M)(?)N_ M_, N∈N,M∈M}; and based on the characterization of rank-one operators in RN RM,i... 详细信息

关键词： Jacobson radical Tensor product Nest algebra

The fundamental solution of the Keldysh typeoperator

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Science china mathematics 2009年第9期52卷 1829-1843页

作者： CHEN ShuXing School of Mathematical sciences, fudan university, shanghai 200433, china School of Mathematical sciences Fudan University Shanghai China

In this paper we discuss the fundamental solution of the Keldysh type operator $ L_\alpha u \triangleq \frac{{\partial ^2 u}} {{\partial x^2 }} + y\frac{{\partial ^2 u}} {{\partial y^2 }} + \alpha \frac{{\partial u}} {{\partial y}} $ , which is a basic mixed type operator different from the Tricomi operator. The fundamental solution of the Keldysh type operator with $ \alpha > - \frac{1} {2} $ is obtained. It is shown that the fundamental solution for such an operator generally has stronger singularity than that for the Tricomi operator. Particularly, the fundamental solution of the Keldysh type operator with $ \alpha < \frac{1} {2} $ has to be defined by using the finite part of divergent integrals in the theory of distributions.

关键词： mixed type equation Keldysh operator fundamental solution finite part of divergent integral 35M10 35A08

CDS Simulation and Pattern Formation of Phase Separation

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Communications in nonlinear Science and Numerical Simulation 1998年第4期3卷 233-236页

作者： Zhanaji LIU Men CHENG Jiong RUAN and Shouji CHENG (Department of Mechanics and Engineering Science, fudan university, shanghai 200433,china)(Department of mathematics, fudan university, shanghai 200433, china) Dept. of Mechanics and Eng. Science Fudan University Shanghai 200433 China Department of mathematics Fudan University Shanghai 200433 China

Several properties of the generation and evolution of phase separating patterns for binary material studied by CDS model are proposed. The main conclusions are (1) for alloys spinodal decomposition, the conceptions of "macro-pattern" and "micropattern" are posed by "black-and- white graph" and "gray-scale graph" *** find that though the four forms of map f that represent the self-evolution of order parameter in a cell(lattice) are similar to each other in "macro-pattern" , there are evident differences in their micro-pattern, e.g., some different fine netted structures in the blackdomain and the white domain are found by the micro-pattern, so that distinct mechanical and physical behaviors shall be obtained. (2) If the two constitutions of block copolymers are not symmetric (i.e. r ≠ 0.5), a pattern called "grain-strip cross pattern"is discovered,in the 0.43 < r < 0.45.

关键词： lattice gas automata CDS phase separation Pattern formation

Jensen's Inequality for Backward Stochastic Differential Equations

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Chinese Annals of mathematics,Series B 2006年第5期27卷 553-564页

作者： Long JIANG Department of mathematics, china university of Mining and Technology, Xuzhou 221008, Jiangsu, china School of Mathematical sciences, fudan university, shanghai 200433, china School of mathematics and System sciences, Shandong university, Jinan 250100, china. Department of mathematics China University of Mining and Technology Xuzhou 221008 Jiangsu China School of Mathematical sciences Fudan University Shanghai 200433 China School of mathematics and System sciences Shandong University Jinan 250100 China

Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen＇s inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g（t, 0）≡ 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen＇s inequality for gexpectation in [4, 7-9].

关键词： Backward stochastic differential equation g-Expectation Jensen's inequality for g-expectation Jensen's inequality for BSDEs

Some New Reductions From a Lax Integrable System

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Acta Mathematicae Applicatae Sinica 2002年第3期18卷 405-410页

作者： En-gui FanInstitute of mathematics. fudan university, shanghai 200433, china Institute of mathematics Fudan University Shanghai China

An isospectral problem with four potentials is discussed. The corresponding hierarchy of Lax integrable evolution equations is derived. For the hierarchy, it is shown that there exist other new reductions except those presented by Tu, Meng and Ma. For each reduction case the relevant Hamiltonian structure is established by means of trace identity.

关键词： Lax integrable system reduction Hamiltonian structure trace identity

Local Existence of Smooth Solutions to the FENE Dumbbell Model

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Chinese Annals of mathematics,Series B 2012年第4期33卷 501-520页

作者： Ge YANG11School of Mathematical sciences, fudan university, shanghai 200433, china. School of Mathematical sciences Fudan University Shanghai China

The author proves the local existence of smooth solutions to the finite extensible nonlinear elasticity (FENE) dumbbell model of polymeric flows in some weighted spaces if the non-dimensional parameter b > 2.

关键词： Fokker-Planck equation FENE model Degenerate parabolic equations Regularity