检索结果-南通市图书馆

Sharpness on the Lower Bound of the Lifespan of Solutions to nonlinear Wave Equations

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of mathematics,Series B 2011年第4期32卷 521-526页

作者： yi zhou 1 Wei HAN 2 1 nonlinear Mathematical Modeling and Methods laboratory shanghai key laboratory for Contem- porary applied mathematics School of Mathematical sciences, Fudan University, shanghai 200433, china. 2 School of Mathematical sciences, Fudan University, shanghai 200433, china Department of mathematics, North University of china, Taiyuan 030051, china. nonlinear Mathematical Modeling and Methods laboratory shanghai key laboratory for contemporary applied mathematics School of Mathematical sciences Fudan University Shanghai China School of Mathematical sciences Fudan University Shanghai China Department of mathematics North University of China Taiyuan China

This paper is devoted to proving the sharpness on the lower bound of the lifespan of classical solutions to general nonlinear wave equations with small initial data in the case n = 2 and cubic nonlinearity （see the results of T. T. Li and Y. M. Chen in 1992）. For this purpose, the authors consider the following Cauchy problem： { where □=δt^2-∑i=1n δx^^2 is the wave operator, g（x）（≡/） 0 is a smooth non-negative function with compact support, and ε 〉 0 is a small parameter. It is shown that the solution blows up in a finite time, and the lifespan T（ε） of solutions has an upper bound T（ε） ≤ exp（Aε-2） with a positive constant A independent of ε, which belongs to the same kind of the lower bound of the lifespan.

关键词： nonlinear wave equation Cauchy problem Lifespan

Global Exact Boundary Controllability for Cubic Semi-linear Wave Equations and Klein-Gordon Equations

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of mathematics,Series B 2010年第1期31卷 35-58页

作者： yi zhou Wei XU Zhen LEI key laboratory of mathematics for nonlinear sciences School of Mathematical Sciences Fudan University Shanghai 200433 China School of Mathematical sciences Fudan University Shanghai 200433 China

The authors prove the global exact boundary controllability for the cubic semilinear wave equation in three space dimensions,subject to Dirichlet,Neumann,or any other kind of boundary controls which result in the well-posedness of the corresponding initial-boundary value *** exponential decay of energy is first established for the cubic semi-linear wave equation with some boundary condition by the multiplier method,which reduces the global exact boundary controllability problem to a local *** proof is carried out in line with [2,15].Then a constructive method that has been developed in [13] is used to study the local *** when the region is star-complemented,it is obtained that the control function only need to be applied on a relatively open subset of the *** the cubic Klein-Gordon equation,similar results of the global exact boundary controllability are proved by such an idea.

关键词： Global exact boundary controllability Cubic semi-linear wave equations The exponential decay Star-shaped Star-complemented Cubic Klein- Gordon equations

Remarks on the Global Existence for Incompressible Navier-Stokes Equations

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of mathematics,Series B 2024年第4期45卷 529-536页

作者： Sheng WANG Zexian ZHANG yi zhou shanghai Center for Mathematical sciences Fudan UniversityShanghai 200433China School of mathematics Science Fudan UniversityShanghai 200433China

In this article,the authors use the special structure of helicity for the threedimensional incompressible Navier-Stokes equations to construct a family of finite energy smooth solutions to the Navier-Stokes equations ... 详细信息

关键词： Navier-Stokes euqations Helicity Global existence Critical norm

(1+2)-Dimensional Radially Symmetric Wave Maps Revisit

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of mathematics,Series B 2022年第5期43卷 785-796页

作者： yi zhou School of Mathematical sciences Fudan UniversityShanghai 200433China

The author gives an alternative and simple proof of the global existence of smooth solutions to the Cauchy problem for wave maps from the(1+2)-dimensional Minkowski space to an arbitrary compact smooth Riemannian manifold without boundary, for arbitrary smooth, radially symmetric data. The author can also treat non-compact manifold under some additional assumptions which generalize the existing ones.

关键词： Cauchy problem Wave maps Global smooth solution

Generalized Persistence of Entropy Weak Solutions for System of Hyperbolic Conservation Laws

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of mathematics,Series B 2022年第4期43卷 499-508页

作者： yi zhou School of Mathematical sciences Fudan UniversityShanghai 200433China

Let u(t,x)be the solution to the Cauchy problem of a scalar conservation law in one space *** is well known that even for smooth initial data the solution can become discontinuous in finite time and global entropy weak solution can best lie in the space of bounded total *** is impossible that the solutions belong to,for example,H^(1) because by Sobolev embedding theorem H^(1) functions are Holder ***,the author notes that from any point(t,x),he can draw a generalized characteristic downward which meets the initial axis at y=α(t,x).If he regards u as a function of(t,y),it indeed belongs to H^(1) as a function of y if the initial data belongs to H^(1).He may call this generalized persistence(of high regularity)of the entropy weak *** main purpose of this paper is to prove some kinds of generalized persistence(of high regularity)for the scalar and 2×2 Temple system of hyperbolic conservation laws in one space dimension.

关键词： Quasilinear hyperbolic system Cauchy problem Entropy weak solution Vanishing viscosity method

A Class of Large Solutions to the 3D Incompressible MHD and Euler Equations with Damping

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2018年第1期34卷 63-78页

作者： yi zhou yi ZHU School of Mathematical sciences Fudan University

In this paper, we derive the global existence of smooth solutions of the 3D incompressible Euler equations with damping for a class of large initial data, whose Sobolev norms H8 can be arbitrarily large for any s ≥0. The approach is through studying the quantity representing the difference between the vortieity and velocity. And also, we construct a family of large solutions for MHD equations with damping.

关键词： Large solutions euler equations MHD equations damping

Global Regularity for Einstein-Klein-Gordon System with U(1)×R Isometry Group,I

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of mathematics,Series B 2020年第6期41卷 939-966页

作者： Haoyang CHEN yi zhou School of Mathematical sciences Fudan UniversityShanghai 200433China

This is the first of the two papers devoted to the study of global regularity of the 3+1 dimensional Einstein-Klein-Gordon system with a U(1)×R isometry *** this first part,the authors reduce the Cauchy problem of the Einstein-Klein-Gordon system to a 2+1 dimensional ***,the authors will give energy estimates and construct the null coordinate system,under which the authors finally show that the first possible singularity can only occur at the axis.

关键词： Einstein-Klein Gordon system Cauchy problem Energy estimates Null coordinate First singularity

在线全文

学校读者我要写书评

暂无评论

基于ML-DMA的黄金期货价格预测研究

数理统计与管理 2024年第3期43卷 541-558页

作者：范彩云童君逸程俊彦周勇上海对外经贸大学统计与信息学院上海201620 统计与数据科学前沿理论及应用教育部重点实验室上海200062 华东师范大学经济与管理学部统计学院和统计交叉科学研究院上海200062

在黄金期货价格预测问题的研究中,价格具有时变性、非线性、高噪声和影响因子复杂等因素,决定了其被准确预测的难度。传统方法对黄金期货价格的预测主要借助于静态模型,导致预测精度不高或分析不足。为了能动态而准确的预测黄金期货价格... 详细信息

在黄金期货价格预测问题的研究中,价格具有时变性、非线性、高噪声和影响因子复杂等因素,决定了其被准确预测的难度。传统方法对黄金期货价格的预测主要借助于静态模型,导致预测精度不高或分析不足。为了能动态而准确的预测黄金期货价格,本文从技术行情指标、行业方面的影响因素及宏观经济环境指标三个维度选取39个变量,以机器学习(machine learning;ML)方法构建基本融合素材,利用动态模型平均(dynamic model averaging,DMA)方法代替传统模型融合技巧,得到黄金期货价格预测模型。实证结果表明,采用机器学习-动态模型平均策略能够明显提高黄金期货价格的预测精度。

关键词：时间序列预测融合模型动态模型平均时变性黄金期货价格

Global Well-Posedness of Incompressible Navier-Stokes Equations with Two Slow Variables

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of mathematics,Series B 2017年第3期38卷 787-794页

作者： Weimin PENG yi zhou College of Science University of Shanghai for Science and Technology School of Mathematical sciences Fudan University

In this paper, the global well-posedness of the three-dimensional incompressible Navier-Stokes equations with a linear damping for a class of large initial data slowly varying in two directions are proved by means of ... 详细信息

关键词： Global well-posedness Incompressible Navier-Stokes equations Slow variables