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ASYMPTOTIC STABILITY OF RAREFACTION WAVE FOR HYPERBOLIC-ELLIPTIC COUPLED SYSTEM IN RADIATING GAS

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Acta Mathematica Scientia 2007年第2期27卷 347-360页

作者：阮立志张晶 laboratory of nonlinear Analysis Department of mathematics Central China Normal University

In this article, author. study the Cauch problem for a model of hyperbolic-elliptic coupled system derived from the one-dimensional system of the rudiating gas. By considering the initial data as a small disturbances of rarefaction wave of inviscid Burgers equation, the global existence of the solution to the corresponding Cauchy problem and asymptotic stability of rarefaction wave is proved. The analysis is based on a priori estimates and L^2-energy method.

关键词： Hyperbolic-elliptic coupled system rarefaction wave asymptotic stability L^2-energy method

Centered Waves for the Two-dimensional Pseudo-Steady van der Waals Gas Satisfied Maxwell's Law Around a Sharp Corner

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Chinese Annals of mathematics,Series B 2024年第4期45卷 537-554页

作者： Shuangrong LI Wancheng SHENG Department of mathematics Shanghai UniversityShanghai 200444China Department of mathematics Zhejiang University of Science and TechnologyHangzhou 310023China corresponding author.Department of mathematics Newtouch Center for Mathematics of Shanghai UniversityShanghai UniversityShanghai 200444China

In this paper,the author. study the centered waves for the two-dimensional(2D for short)pseudo-steady supersonic flow with van der Waals gas satisfied Maxwell's law around a sharp *** view of the initial value of the specific volume and the properties of van der Waals gas,the centered waves at the sharp corner are constructed by *** is shown that the supersonic incoming flow turns the sharp corner by a centered simple wave or a centered simple wave with right-contact discontinuity or a composite wave(jump-fan,fan-jump or fan-jump-fan),or a combination of waves and constant ***,the critical angle of the sharp corner corresponding to the appearance of the vacuum phenomenon is obtained.

关键词： Two-dimensional Euler equations Van der Waals gas Centered simple wave Composite wave

The Riemann Problem for Chaplygin Gas Flow in a Duct with Discontinuous Cross-Section

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Chinese Annals of mathematics,Series B 2020年第4期41卷 531-546页

作者： Liancheng DANG Wancheng SHENG Department of mathematics Shanghai UniversityShanghai 200444China. corresponding author.Department of mathematics Shanghai UniversityShanghai 200444China.

The fluid flows in a variable cross-section duct are nonconservative because of the source ***,the Riemann problem and the interactions of the elementary waves for the compressible isentropic gas in a variable cross-section duct were *** this paper,the Riemann problem for Chaplygin gas flow in a duct with discontinuous cross-section is *** elementary waves include rarefaction waves,shock waves,delta waves and stationary waves.

关键词： Duct flow Chaplygin gas equations Nonconservative Riemann problem Delta wave Stationary wave

Turnpike Properties for Stochastic Linear-Quadratic Optimal Control Problems

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Chinese Annals of mathematics,Series B 2022年第6期43卷 999-1022页

作者： Jingrui SUN Hanxiao WANG Jiongmin YONG Department of mathematics Southern University of Science and TechnologyShenzhen 518055China corresponding author.College of mathematics and Statistics Shenzhen UniversityShenzhen 518060China Department of mathematics University of Central FloridaOrlandoFL 32816USA

This paper analyzes the limiting behavior of stochastic linear-quadratic optimal control problems in finite time-horizon[0,T]as T→∞.The so-called turnpike properties are established for such problems,under stabilizability condition which is weaker than the controllability,normally imposed in the similar problem for ordinary differential *** dealing with the turnpike problem,a crucial issue is to determine the corresponding static optimization *** mimicking the deterministic situations,it seems to be natural to include both the drift and the diffusion expressions of the state equation to be zero as constraints in the static optimization ***,this would lead us to a wrong *** is found that the correct static problem should contain the diffusion as a part of the objective function,which reveals a deep feature of the stochastic turnpike problem.

关键词： Turnpike property Stochastic optimal control Static optimization Linear-quadratic Stabilizability Riccati equation

Construction of Lagrangian Submanifolds in Complex Hyperquadric

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Chinese Annals of mathematics,Series B 2020年第3期41卷 465-478页

作者： Chiakuei PENG Xiaowei XU School of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China corresponding author.School of Mathematical sciences and Wu Wen-Tsun Key laboratory of mathematics University of Science and Technology of ChinaHefei 230026China

In this paper, the author. present a method to construct the minimal and H-minimal Lagrangian submanifolds in complex hyperquadric Q_n from submanifolds with special properties in odd-dimensional spheres. The author. ... 详细信息

关键词： Lagrangian submanifold Minimal H-minimal

L^p-decay rates to nonlinear diffusion waves for p-system with nonlinear damping

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science China mathematics 2006年第6期49卷 721-739页

作者： ZHU Changjiang JIANG Mina laboratory of nonlinear Analysis Department of Mathematics Central China Normal University Wuhan 430079 China Laboratory of Nonlinear Analysis Department of Mathematics Central China Normal University Wuhan 430079 China

In this paper, we study the Lp (2≤p≤ +∞) convergence rates of the solutions to the Cauchy problem of the so-called p-system with nonlinear damping. Precisely, we show that the corresponding Cauchy problem admits a unique global solution (v (x,t), u(x, t)) and such a solution tends time-asymptotically to the corresponding nonlinear diffusion wave ((v|-)(x,t),(u|-)(x,t)) governed by the classical Darcy's law provided that the corresponding prescribed initial error function lies in and is sufficiently small. Furthermore, the Lp (2≤p≤ +∞) convergence rates of the solutions are also obtained.

关键词： nonlinear damping, nonlinear diffusion waves, convergence rates, energy estimates.

A Schwarz Lemma at the Boundary of Hilbert Balls

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Chinese Annals of mathematics,Series B 2018年第4期39卷 695-704页

作者： Zhihua CHEN Yang LIU Yifei PAN Department of mathematics Tongji UniversityShanghai 200092 China. corresponding author. Department of mathematics Zhejiang Normal University Jinhua 321004Zhejiang China. Department of Mathematical sciences Indiana University-Purdue University Fort Wayne Fort Wayne IN 46805-1499 USA School of mathematics and Informatics Jiangxi Normal University Nanchang 330022 China.

In this paper, the author. prove a general Schwarz lemma at the boundary for the holomorphic mapping f between unit balls B and B＇ in separable complex Hilbert spaces H and H＇, respectively. It is found that if the mapping f ∈ C^1＋α at z0 ∈ B with f（zo） = wo ∈ OB＇, then the Fr＆het derivative operator Df（z0） maps the tangent space Tz0（ B^n） to Tw0（ B＇）, the holomorphic tangent space Tz0^（1,0） to Tw0（1,0）（ B＇）,respectively.

关键词： Boundary Schwarz lemma Separable Hilbert space Holomorphic mapping Unit ball

Flow of Burgers' fluid over an inclined stretching sheet with heat and mass transfer

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Journal of Central South University 2015年第8期22卷 3180-3188页

作者： T.Hayat Sadia Asad A.Alsaedi Department of mathematics Quaid-i-Azam University nonlinear Analysis and Applied mathematics (NAAM) Research Group Department of Mathematics Faculty of Science King Abdulaziz University

Effects of heat and mass transfer in the flow of Burgers fluid over an inclined sheet are discussed. Problems formulation and relevant analysis are given in the presence of thermal radiation and non-uniform heat source/sink. Thermal conductivity is taken temperature dependent. The nonlinear partial differential equations are simplified using boundary layer approximations. The resultant nonlinear ordinary differential equations are solved for the series solutions. The convergence of series solutions is obtained by plotting theη-curves for the velocity, temperature and concentration fields. Results of this work describe the role of different physical parameters involved in the problem. The Deborah numbers corresponding to relaxation time(β1 and β2) and angle of inclination(α) decrease the fluid velocity and concentration field. Concentration field decays as Deborah numbers corresponding to retardation time(β3) and mixed convection parameter(G) increase. Large values of heat generation/absorption parameters A/B, and the temperature distribution across the boundary layer increase. Numerical values of local Nusselt number,-θ′(0), and local Sherwood number,-f′(0), are computed and analyzed. It is found that θ′(0) increases with an increase in β3.

关键词： Burgers' fluid thermal radiation inclined stretching sheet non-uniform heat source variable thermal conductivity

An Explicit Example of a Reich Sequence for a Uniquely Extremal Quasiconformal Mapping

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Chinese Annals of mathematics,Series B 2021年第3期42卷 327-332页

作者： Xue MENG Sihui ZHANG College of science University of Shanghai for Science and TechnologyShanghai 200093China corresponding author.College of science University of Shanghai for Science and TechnologyShanghai 200093China

An explicit example of a Reich sequence for a uniquely extremal quasiconformal mapping in a borderline case between uniqueness and non-uniqueness is given.

关键词： Quasiconformal mapping Uniquely extremal quasiconformal mapping Reich sequence