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Global Classical Solutions to Partially Dissipative Quasilinear Hyperbolic Systems

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Chinese Annals of Mathematics,Series B 2011年第5期32卷 771-780页

作者： Yi ZHOU 11 Key Laboratory of Mathematics for Nonlinear sciences,Ministry of Education,china.shanghai Key Laboratory for Contemporary Applied Mathematics school of mathematical sciences,fudan university,shanghai 20043.,china. Key Laboratory of Mathematics for Nonlinear sciences Ministry of Education China shanghai Key Laboratory for Contemporary Applied Mathematics school of mathematical sciences Fudan University Shanghai China

The author considers the Cauchy problem for quasilinear inhomogeneous hyperbolic *** the assumption that the system is weakly dissipative,Hanouzet and Natalini established the global existence of smooth solutions for small initial data (in *** ***.,Vol.169,2003,pp.89-117).The aim of this paper is to give a completely different proof of this result with slightly different assumptions.

关键词： Cauchy problem Global classical solution Partially dissipativequasilinear hyperbolic system

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 20043., 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

Solid Desiccant Heat Pump Fresh Air Unit using Composite Silica gel

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Journal of Thermal Science 2024年第4期33卷 1286-1300页

作者： yang Tianyu GUO Defang ge Tianshu Institute of Refrigeration and Cryogenics Shanghai Jiao Tong UniversityKey Laboratory of Power Mechanical EngineeringMOE ChinaShanghai200240China Qingdao Haier A/C Electronic Co. LtdQingdao266101China

The introduction of fresh air into the indoor space leads to a significant increase in cooling or heating *** desiccant heat pump fresh air unit which can handle the latent and sensible load of fresh air efficiently have been proposed *** improve the performance of the solid desiccant heat pump fresh air unit in the fresh air handling process,in this paper,the application of composite silica gel in a heat pump fresh air unit was *** comparison between silica gel coating(SGC)and composite silica gel coating(CSGC)shows that the adsorption rate and water uptake capacity of CSGC are more than two times higher than those of *** experimental setup for the solid desiccant heat pump fresh air unit was *** performance of SGC and CSGC was tested in the setup *** show that under summer conditions,compared with the solid desiccant heat pump fresh air unit using silica gel(SGFU),the average moisture removal and COP of the one using composite silica gel(CSGFU)increased by 15%and 30%,*** winter conditions,compared with SGFU,the average humidification and COP of CSGFU increased by 42%and 17%.With optimal operation conditions of 3 min switchover time and 40 r/s compressor frequency,the COP of CSGFU under summer conditions can reach *** also show that the CSGFU and SGFU have higher COP and dehumidification rate under higher outdoor temperature and humidity ratio.

关键词： fresh air system desiccant coated heat exchanger humidification dehumidification experimental comparison

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

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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 20043., china. 2 school of mathematical sciences, fudan university, shanghai 20043., 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

THE DISTANCE BETWEEN DIFFERENT COMPONENTS OF THE UNIVERSAL TEICHMULLER SPACE

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Chinese Annals of Mathematics,Series B 2005年第4期26卷 537-542页

作者： WANG ZHE school of mathematical sciences Fudan University Shanghai 200433 China.

The model of the universal Teichmuller union of infinite disconnected components. between different components is 0, and the every other component is 2. space by the derivatives of logarithm is the In this paper, it i... 详细信息

关键词： Universal Teichmuller space Logarithmic derivative Quasiconformal extension

Blow Up of Solutions to Semilinear Wave Equations with Critical Exponent in High Dimensions

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Chinese Annals of Mathematics,Series B 2007年第2期28卷 205-212页

作者： Yi ZHOU school of mathematical sciences Fudan University Shanghai 200433 China

In this paper, the author considers equations with critical exponent in n ≥4 space tions on the initial data, it is proved that there small the initial data are. the Cauchy problem for semilinear wave dimensions. Und... 详细信息

关键词： Semilinear wave equation Critical exponent Cauchy problem Blow up

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 20043., 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 > - \fracge ge $ 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 ge ge $ 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

RADIAL BASIS FUNCTION INTERPOLATION IN SOBOLEV SPACES AND ITS APPLICATIONS

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Journal of Computational Mathematics 2007年第2期25卷 201-210页

作者： Manping Zhang (school of mathematical sciences,fudan university,shanghai 20043.,china.Institute of Computational Mathematics,Chinese Academy of sciences,Beijing 100080,china school of mathematical sciences fudan university Shanghai 200433

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space H^k（Ω）（k 〉 1）. With a special kind of radial basis function, we construct a basis in H^k（Ω） and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density.

关键词： Sobolev space Radial basis function Global data density Meshless method

Terminal attitude selection method of missile attack aircraft

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Chinese Journal of Aeronautics 2024年第2期37卷 385-400页

作者： Peng HOU yang PEI Yuxue ge Mengjie ZHU school of Aeronautics Northwestern Polytechnical UniversityXi’an 710072China Research Department Shanghai Electro-Mechanical Engineering InstituteShanghai 201108China

The appropriate terminal attitude of missile is important to improve the damage effectiveness of fragmentation warhead against aircraft *** this paper,three missile terminal attitude selection methods are proposed to solve the problem of terminal attitude selection in different situations according to their respective evaluation *** MVE-based method uses the damage probability of each detonation point around the aircraft at a given attitude of missile to calculate the Mean Volume of Effectiveness(MVE)at the corresponding attitude,and then uses the MVE for different attitudes to select the terminal strike *** detonation position-based method addresses the case where the missile detonation position can be assessed in *** the effects of missile guidance errors and fuze activation position errors,Monte Carlo simulations are used to calculate the damage probability of aircraft with different strike attitudes,from which the terminal strike attitude is *** BP-ANN model-based method uses the constructed Back Propagation Artificial Neural Network(BP-ANN)model instead of simulation to calculate the evaluation indexes in the corresponding cases of MVE-based method and Detonation position-based method,which can improve the efficiency of attitude *** are conducted for different scenarios to verify the feasibility and effectiveness of the proposed method.

关键词： Aircraft vulnerability Attitude selection BP-ANN Damage probability Damage effectiveness