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Gevrey Class Regularity and exponential decay Property for Navier-Stokes-α Equations

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Acta Mathematicae Applicatae Sinica 2007年第1期23卷 49-58页

作者： Yong-jiang Yu Kai-tai Li Ai-xiang Huang Department of Mathematics Shanghai Jiaotong University Shanghai 200240 China Department of Mathematics Xi'an Jiaotong University Xi'an 710049 China

The Navier-Stokes-α equations subject to the periodic boundary conditions are considered. Analyticity in time for a class of solutions taking values in a Gevrey class of functions is proven. exponential decay of the spatial Fourier spectrum for the analytic solutions and the lower bounds on the rate defined by the exponential decay are also obtained.

关键词： Gevrey class regularity Navier-Stokes-α equations exponential decay

exponential decay FOR A NONLINEAR VISCOELASTIC EQUATION WITH SINGULAR KERNELS

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Acta Mathematica Scientia 2012年第6期32卷 2237-2246页

作者： Shun-Tang Wu General Education Center National Taipei University of Technology Taipei 106~ China

The nonlinear viscoelastic wave equation ｜μt｜^pμtt-△μ-μutt＋∫^t0g（t-s）△μ（s）ds＋｜μ｜^pU=0,in a bounded domain with initial conditions and Dirichlet boundary conditions is consid- ered. We prove that, for a class of kernels 9 which is singular at zero, the exponential decay rate of the solution energy. The result is obtained by introducing an appropriate Lyapounov functional and using energy method similar to the work of Tatar in 2009. This work improves earlier results.

关键词： viscoelastic wave equation kernel exponential decay memory term singular kernel

exponential decay of expansive constants

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Science China Mathematics 2013年第10期56卷 2063-2067页

作者： SUN Peng China Economics and Management Academy Central University of Finance and Economics

A map f on a compact metric space is expansive if and only if fn is *** study the exponential rate of decay of the expansive constant of fn and find some of its relations with other quantities about the dynamics,such ... 详细信息

关键词： expansive expansive constant generator exponential decay Lebesgue number box dimension topological entropy

exponential decay DOMAIN OF ENERGY FOR WAVE EQUATION UNDER FEEDBACK CONTROL

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Acta Mathematicae Applicatae Sinica 1999年第3期15卷 249-256页

作者：张维弢冯德兴 Institute of Systems Science the Chinese Academy of Sciences Beijing China

This paper deals with the energy estimate of wave equation with boundary and distributedfeedback action. It is shown that the energy of the system decays exponentially if the feedback parameters are in some domain (i.e., the so-called exponential decay domain). And thedependence on the feedback parameters of the energy exponeatial decay estimate is obtained.

关键词： Wave equation boundary feedback distributed feedback energy estimate exponential decay

GLOBAL STRONG SOLUTION AND exponential decay OF 3D NONHOMOGENEOUS ASYMMETRIC FLUID EQUATIONS WITH VACUUM

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Acta Mathematica Scientia 2021年第5期41卷 1428-1444页

作者： Guochun WU Xin ZHONG Fujian Province University Key Laboratory of Computational Science School of Mathematical SciencesHuaqiao UniversityQuanzhou 362021China School of Mathematics and Statistics Southwest UniversityChongqing 400715China

We prove the global existence and exponential decay of strong solutions to the three-dimensional nonhomogeneous asymmetric fluid equations with nonnegative density provided that the initial total energy is suitably *** that although the system degenerates near vacuum,there is no need to require compatibility conditions for the initial data via time-weighted techniques.

关键词： nonhomogeneous asymmetric fluid equations global strong solution exponential decay vacuum

exponential decay H∞ Load Torque Observer of Permanent Magnet Synchronous Motor

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Exponential Decay H∞ Load Torque Observer of Permanent Magn...

Global Existence and exponential decay for a Nonlinear Viscoelastic Equation with Nonlinear Damping

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作者： Dazhou Peng School of Automation Science and Engineering South China University of Technology

The load torque observation issue for permanent magnet synchronous motor(PMSM) is studied in the paper,and a design method for exponential decay H load torque observer is *** H disturbance rejection rate and the exponential decay rate of observation error can be specified through the studied designed *** the required disturbance rejection and dynamic responsibility performance can both be met by the obtained load torque *** control performance of motor speed can be improved by the torque feed-forward compensation base on this *** experiment result approved the validity of studied method.

关键词： Load Torque Observer H∞ Observer exponential decay Permanent Magnet Synchronous Motor

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Journal of Partial Differential Equations 2009年第4期22卷 299-314页

作者： HAN Xiaosen Institute of Contemporary Mathematics and School of Mathematics and Information Science Henan University Kaifeng 475001 China.

In this paper we investigate a nonlinear viscoelastic equation with nonlinear damping. Global existence of weak solutions and uniform decay of the energy have been established. The Faedo-Galerkin method and the pertur... 详细信息

关键词： Global existence exponential decay nonlinear viscoelastic equation.

Pharmacokinetic analysis of combined multibottle infusion in an exponential decay pattern

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Pharmacokinetic analysis of combined multibottle infusion in...

GLOBAL EXISTENCE, UNIFORM decay AND exponential GROWTH FOR A CLASS OF SEMI-LINEAR WAVE EQUATION WITH STRONG DAMPING

中国药理学会临床药理学专业委员会会议暨第十次全国临床药理学学术会议

作者： XIE Hai-tang~1 HUANG Xiao-hui~2 SONG Jian-guo~3 SUN Rui-yuan~1 1 Anhui Provincial Centre for Drug Clinical Evaluation,Yijishan Hospital,Wannan Medical College,Wuhu 241001,Anhui,China 2 Center of Pharmacokinetics,College of Pharmacy,Anhui Medical University,Hefei 230032,Anhui,China 3 Department of Pharmacology,Wannan Medical College,Wuhu 241000,Anhui,China

To study the rational and scientific way of adminis- trating the drugs whose pharmacokinetics conform to three- compartment open *** on the double-bottle ex- ponential decay infusion introduced by Sun Rui-yuan and Song Jian-guo,this manuscript describe the comabined multi-bottle exponential decay infusion(CMI)in achieving optimal plasma drug concentration thai ensure adequate therapeutic effects in the absence of significant side effects and a rapid return of ***’s transformation was applied to verify group of equations listed according to the specific apparatus and the three compartments with elimination occurs mainly through central compartment, which yields the following equations used in calculating the volumes and concentration of bottle A,B and P respective- ly: C=(CssVK/d);Cbo=(CadK/αβ)(α+β-K);Vb =(d/K);Cpo=(Caπ)/10;Vp=(d/K;C(t)=(dCa/KV)(1-e). It is estirnated that the plasma concentration against time curve of the CMI is the function in mathematics of pai(π), the fast distribution rate constant while in the situation of conventional mono-bottle infusion,the C-T curve is the function in mathematics of beta(β),the slow distribution rate *** pharmacokinetic parameters were obtained and used for calculating the appropriate volumes and concentrations of each bottle *** has verified by animal experiment that the target plasma propofol levels (measured using HPLC)were rapidly attained and main- mined as desired,thus provided an alternative method of drug delivery.

关键词： Combined Multi-bottle Infusion(CMI) exponential decay propofol HPLC

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Acta Mathematica Scientia 2013年第1期33卷 41-58页

作者：陈化刘功伟 School of Mathematics and Statistics Wuhan University

In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 〈 E（0）〈 d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E（0）〈 0.

关键词： strong damping nonlinear damping global existence polynomial decay exponential decay exponential growth