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An Improved Strategy in Controlling Chaotic Dynamics to Any Desired Orbit

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Communications in nonlinear Science and Numerical Simulation 1998年第1期3卷 31-35页

作者： Lijuan LI, Xiping ZENG and Jiong RUAN, Zhenxun HUANG (institute of mathematics,{2., shanghai 200433) institute of mathematics Fudan University Shanghai 200433 China

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关键词： Strategy Improved Chaotic Any An

DIRECT CONSTRUCT OF PERIODIC SOLUTIONS TO PERTURBED KLEIN-GORDON EQUATIONS BY NEWTON ITERATION

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Chinese Annals of mathematics,Series B 2000年第3期21卷 297-322页

作者： SHI YUMING (Department of mathematics, fudan university,{2., china. E-mail: ymshi@***) Department of mathematics Fudan University Shanghai 200433 China

By introducing the block estimate technique and directly using the Newton iteration method, the author constructs Cantor families of time periodic solutions to a class of nonlinear wave equations with periodic boundary conditions. The Lyapunov-Schmidt decomposition used by J. Bourgain, W. Craig and C. E. Wayne is avoided. Thus this work simplifies their framework for KAM theory for PDEs.

关键词： Klein-Gordon equation Periodic solution Newton iteration

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

GLOBAL EXISTENCE OF WEAKLY DISCONTINUOUS SOLUTIONS TO A KIND OF MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS

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Applied mathematics(A Journal of Chinese Universities) 2007年第2期22卷 181-200页

作者： Guo Fei School of Mathematical sciences, fudan university,{2., china Department of mathematics, Qufu Normal university, Shandong, 2.3165, china. School of Mathematical sciences Fudan University Shanghai China Department of mathematics Qufu Normal University Shandong China

In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {（t, x）｜ t ≥ 0, x ≥0} is considered. A suffic... 详细信息

关键词： quasilinear hyperbolic system mixed initial-boundary value problem global weakly discontinu-ous solution weak linear degeneracy

THE REGULARITY OF SOLUTIONS FOR nonlinear DEGENERATE ELLIPTIC BOUNDARY VALUE PROBLEM

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Chinese Annals of mathematics,Series B 1990年第3期11卷 330-341页

作者：洪家兴 institute of mathematics Fudan University

This paper is devoted lo the study of regularity of solutions for Dirichlet probelm ofnonlinear degenerate elliptic equations in two dimensional case. A sufficient condition fortheir solutions in C3+α（Ω） to be cer... 详细信息

关键词： regularity elliptic degenerate devoted Dirichlet proof Nirenberg grateful implies milar

Mean Curvature Flow via Convex Functions on Grassmannian Manifolds

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Chinese Annals of mathematics,Series B 2010年第3期31卷 315-328页

作者： Yuanlong XIN Ling YANG institute of mathematics Fudan University Shanghai 200433 China. Max Planck institute for the mathematics in {2. Inselstr. 22-24 Leibzig 04103 Germany.

Using the convex functions on Grassmannian manifolds, the authors obtain the interior estimates for the mean curvature flow of higher codimension. Confinable properties of Gauss images under the mean curvature flow have been obtained, which reveal that if the Gauss image of the initial submanifold is contained in a certain sublevel set of the v-function, then all the Gauss images of the submanifolds under the mean curvature flow are also contained in the same sublevel set of the v-function. Under such restrictions, curvature estimates in terms of v-function composed with the Gauss map can be carried out.

关键词： Mean curvature flow Convex function Gauss map

GEOMETRIC INEQUALITIES FOR CERTAIN SUBMANIFOLDS IN A PINCHED RIEMANNIAN MANIFOLD

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Acta Mathematica Scientia 2007年第3期27卷 611-618页

作者：谢纳庆许洪伟 institute of mathematics Fudan University Center of Mathematical sciences Zhejiang University

This article gives some geometric inequalities for a submanifold with parallel second fundamental form in a pinched Riemannian manifold and the distribution for the square norm of its second fundamental form.

关键词： Submanifolds second fundamental form pinched Riemannian manifold

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,{2., 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

LIFE-SPAN OF CLASSICAL SOLUTIONS TO ONE DIMENSIONAL nonlinear WAVE EQUATIONS

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Chinese Annals of mathematics,Series B 1992年第3期13卷 266-279页

作者：李大潜俞新周忆 institute of mathematics Fudan UniversityShanghai 200433China. Department of Applied mathematics Tongji UniversityShanghai 200092China.

By means of a simple and direot method,the authors obtain the sharp lower bound ofthe life-span of classioal solutions to the Cauohy problem with small initial data for onedimensional fully nonlinear wave equations ut... 详细信息

关键词： WAVE sharp affine verified 云一岁夕 integer applying desired satisfy