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ON THE EQUATION□Φ=|▽Φ|~2 IN FOUR SPACE DIMENSIONS

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Chinese Annals of mathematics,Series B 2003年第3期24卷 293-302页

作者： zhou yi institute of mathematics, fudan university, shanghai 200433, china.

This paper considers the following Cauchy problem for semilinear wave equations in n space dimensionswhere A is the wave operator, F is quadratic in (?) with (?) = ( ).The minimal value of s is determined such that the above Cauchy problem is locally well-posed in H8. It turns out that for the general equation s must satisfyThis is due to Ponce and Sideris (when n = 3) and Tataru (when n≥5). The purpose of this paper is to supplement with a proof in the case n = 2,4.

关键词： Semilinear wave equation Cauchy problem Low regularity solution

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

PARAMETERS OF DARBOUX TRANSFORMATION FOR REDUCED AKNS,KAUP-NEWELL AND PCF SYSTEMS

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Chinese Annals of mathematics,Series B 1999年第2期20卷 195-204页

作者： zhou ZIXIANG(institute of mathematics, fudan university, shanghai 200433) fudan Univ Inst Math Shanghai 200433 Peoples R China

FOr the integrable system with u(p, q) reduction, there is a well-known sufficient conditionto choose the parameters: the spectral parameters only take two mutually conjugate valuesand the solutions of the Lax pair should satisfy certain orthogonal relations. In this paper, theauthor proves that, for the AKNS system, the Kaup-Newed system and the principal chiralfield (PCF), this condition is also necessary for generic potentials with the u(p, q) *** some other reductions, sufficiency and necessity of more constraints are proved.

关键词： Darboux transformation Spectral parameters u(p q) reduction

THE MODULI SPACE OF COMPLEX LAGRANGIAN SUBMANIFOLDS IN THE HYPER-KAEHLER MANIFOLD

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Chinese Annals of mathematics,Series B 1999年第4期20卷 393-400页

作者： FU JIXIANG(institute of mathematics, fudan university, shanghai 200433, china) fudan Univ Inst Math Shanghai 200433 Peoples R China

The deformation of a compact complex Lagrangian submanifold in a hyper-Kaehler manifold and the moduli space are studied. It is proved that the moduli space Mc1 is a special Kaehler manifold, where special means that there is a real flat torsionfree symplectic connection satisfying dI = 0 (I is a complex structure of Mcl). Thus, following [4], one knows thatT*Mcl is a hyper-Kaehler manifold and then that Mcl is a complex Lagrangian submanifold in T* Mcl.

关键词： Moduli space Complex Lagrangian submanifold Hyper-Kaehler manifold Special Lagrangian submanifold Special Kaehler manifold Deformation

THE OCCUPATION DENSITY FIELD FOR THE CATALYTIC SUPER-BROWNIAN MOTION

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Chinese Annals of mathematics,Series B 1999年第4期20卷 447-454页

作者： HONG WENMING(institute of mathematics, fudan university shanghai 200433, china) fudan Univ Inst Math Shanghai 200433 Peoples R China

It is proved that the occupation time of the catalytic super-Brownian motion is absolutely continuous for d = 1, and the occupation density field is jointly continuous and jointly Holder continuous.

关键词： Branching rate functional Brownian collision local time Catalytic super-Brownian motion Occupation time Occupation density field

GLOBAL CLASSICAL SOLUTIONS WITH SMALL INITIAL TOTAL VARIATION FOR QUASILINEAR HYPERBOLIC SYSTEMS

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Chinese Annals of mathematics,Series B 2002年第3期23卷 335-348页

作者： YAN PING institute of mathematics, fudan university, shanghai 200433, china institute of mathematics Fudan University Shanghai 200433 China

By means of the continuous Glimm functional, a proof is given on the global existence of classical solutions to Cauchy problem for general first order quasilinear hyperbolic systems with small initial total variation.

关键词： Weak linear degeneracy Continuous Glimm functional Total variation Global classical solution Quasilinear hyperbolic system

ON A CONSTRUCTION OF INERTIALMANIFOLDS FOR A CLASS OF SECOND ORDER IN TIME EVOLUTION EQUATIONS

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Chinese Annals of mathematics,Series B 1999年第3期20卷 271-278页

作者： WANG ZONGXIN(institute of mathematics, fudan university, shanghai 200433, china.) fudan Univ Inst Math Shanghai 200433 Peoples R China

Inertial manifolds for a class of second order in time dissipative equations are *** author also proves an asymptotic completeness property for the inertial manifolds and characterizes the inertial manifolds as the set of trajectories whose growth is at most of order O(e-μt ) for some p > 0. As applications, a nonlinear wave equation and a problem of nonlinear oscillations of a shallow shell are considered.

关键词： Dynamical systems Inertial manifolds Nonlinear evolution equations

ON INTERACTION OF SHOCK AND SOUND WAVE (Ⅰ)

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Chinese Annals of mathematics,Series B 1996年第4期17卷 35-42页

作者： CHEN SHUXING(institute of mathematics, fudan university shanghai 200433, china.) 复旦大学数学系上海

This paper studies the ioteraction of shock and gradient wave (sound wave) of solutions to the system of inviscid isentropic gas dynamics as a model for the corresponding problems for nonlinear hyperbolic systems. The problem can be reduced to a boundary value problem in a wedged domain. By using the method of constructing asymptotic solutions and Newton’s iteration process it is proved that if a weak shock hits a gradient wave, then the grandient wave will split into two gradient waves, while the shock continuses propagating. In this paper the author reduces the problem to a standard form and constructs asymptotic solution of the problem. The existence of the genuine solution will be given in the following paper.

关键词： Shock wave Sound wave Nonliner hyperbolic system Asymptotic solution

Averaging of Hamilton-Jacobi equation in infinite dimensions and application

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Chinese Science Bulletin 1998年第1期43卷 30-32页

作者： WANG Shihong institute of mathematics, fudan university, shanghai 200433, china fudan university Institute of Mathematics Shanghai China

The averaging of Hamilton_Jacobi equation with fast variables in viscosity solution sense in infinite dimensions is studied. It is proved that viscosity solution of the original equation converges to viscosity solution of the averaged equation and this result is applied to study the limit problem of the value function for optimal control problem with fast variables.

关键词： infinite dimensions averaging of HJB equation viscosity solution optimal control problem value function.