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uniform stability AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF 2-DIMENSIONAL MAGNETOHYDRODYNAMICS EQUATIONS

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Chinese Annals of Mathematics,Series B 1998年第1期19卷 35-58页

作者： ZHANG LINGHAI Department of Mathematics The Ohio State UniversityColumbusOhio43210USA.

This paper is concerned with uniform stability and asymptotic behavior for solutions of 2-dimensional Magnetohydrodynamics equations. The author establishes the corresponding temporal decay estimates when the initial data is in the following Sobolev spaces H 2, L 1∩H 2 with ∫(u 0, A 0)dx≠0, or L 1∩H 2 with ∫(u 0, A 0)dx=0, respectively. Most of the decay rates in these estimates are optimal. Moreover, the author proves various uniform stability results, like  sup t>0 ‖(w, E, r)(t))‖ YC‖(w 0, E 0)‖ X, where X and Y are Sobolev spaces. It should be pointed out that the decay estimates of the solutions for the case (u 0, A 0)∈L 1∩H 2 follow from the uniform stability estimates. The author utilizes the Fourier splitting method invented by Professor Schonbek and the new elaborate global energy estimates.

关键词： uniform stability Asymptotic behavior Magnetohydrodynamics equations Fourier transform Energy estimates

SHARP CONDITIONS FOR THE uniform stability OF NONAUTONOMOUS HUTCHINSON'S EQUATION

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Annals of Differential Equations 2004年第2期20卷 194-207页

作者：庚建设 Dept of Math Guangzhou University Guangzhou 510405

In this paper we obtain new criteria for the positive equilibrium K of thenonautonomous Hutchinson's equationN'(t) = r(t)N(t)[1-[N(t-τ)]/K], t≥0,to be uniformly stable. Examples illustrating the significance of the ... 详细信息

关键词： Hutchinson's equation uniform stability time delay

On uniform stability of nonlinear measure differential equations

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On uniform stability of nonlinear measure differential equat...

ASYMPTOTIC stability FOR A CLASS OF NONAUTONOMOUS NEUTRAL DIFFERENTIAL EQUATIONS

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作者： Yueju Cao Department of Mathematics College of General EducationShanghai Jianqiao University

This paper investigates uniform stability and uniformly asymptotical stability of nonlinear measure differential equations in Banach spaces. This general system can model a large class of hybrid systems without any restriction on their Zeno behavior. The sufficient conditions of uniform stability and uniformly asymptotical stability for the system are obtained by using Lyapunov functions, in the lack of Lipschitz continuity assumptions. Then less conservative stability criteria for impulsive differential equations than those in the literature are deduced as a special case.

关键词： measure differential equations uniform stability asymptotical stability Henstock-Lebesgue-Stieltjes integral regulated functions

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Chinese Annals of Mathematics,Series B 1997年第4期18卷 449-456页

作者： YU JIANSHE Department of Applied Mathematics Hunan UoiversityChangeha 410082China

Consider the scalar nonlinear delay differential equationddt[x(t)-f(t,x(t-τ))]+g(t,x(t-δ))=0,tt 0,where τ,δ(0,∞),f,gC([t 0,∞)×R,R)and xg(t,x)0 for tt 0,x∈*** author obtains sufficient conditi... 详细信息

关键词： Neutral equation uniform stability Asymptotic stability

stability of Second Order Differential Equation Disturbed with Delays

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Journal of Donghua University(English Edition) 2005年第3期22卷 106-110页

作者：高国柱叶海平俞成 Department of Applied Mathematics Donghua UniversityShanghai 200051

In this paper, stability problems for the second order nonlinear differential equations disturbed with delays are studied. By means of the new stability theorems and Liapunov functional, the authors obtain some result... 详细信息

关键词： uniform stability asymptotic stability functional differential equations Liapunov functional

Extremal Kähler Metrics of Toric Manifolds

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Chinese Annals of Mathematics,Series B 2023年第6期44卷 827-836页

作者： An-Min LI Li SHENG Department of Mathematics Sichuan UniversityChengdu 610065China

This paper is a survey of some recent developments concerning extremal Kähler metrics on Toric Manifolds.

关键词： Extremal K¨ahler metric Toric manifolds Kb-stability uniform stability

uniform DECAY IN WEAKLY DISSIPATIVE TIMOSHENKO SYSTEM WITH INTERNAL DISTRIBUTED DELAY FEEDBACKS

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Acta Mathematica Scientia 2016年第3期36卷 815-830页

作者： Tijani A. APALARA Department of Mathematics University of Hafr AI-Batin (UoHB) Hafr AI-Batin 31991 Saudi Arabia

In this paper we consider one-dimensional Timoshenko system with linear fric- tional damping and a distributed delay acting on the displacement equation. Under suitable assumptions on the weight of the delay and the wave speeds, we establish the well-posedness of the system and show that the dissipation through the frictional damping is strong enough to uniformly stabilize the system even in the presence of delay.

关键词： Timoshenko system well-posedness uniform stability distributed delay

A New Idea of stability Theory of Motion and Its Application

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Progress in Natural Science:Materials International 1993年第4期 341-351页

作者：李森林张孟秋 Changsha 410012 Department of Mathematics Hunan University Hunan Educational Institute PRC

In this paper,a new idea of stability theory is *** first,we obtain the sufficient condi-tions of uniform stability,asymptotical stability and nonstability of zero solution of n-dimensionalnonautonomous *** conditions can be used conveniently in practicai applications,The study onthe stability of large system in this paper,compared with the previous literature,shows the advantages of *** result in the critical case,which we denved at last,cannot be gotten by the method.

关键词： n-dimensional nonautonomous system uniform stability asymptotical stability nonstability

uniformLY ASYMPTOTIC stability FOR DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

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Annals of Differential Equations 2002年第2期18卷 107-116页

作者：陈武华卢小梅

One-dimensional differential equations of the form x'(t) + λx(t) = F(t, xt) areconsidered assuming that λ> 0 and that F satisfies either -or a condition in which N is replaced by M, wheremax, and μis bounded, nondecre-asing and is left continuous on [0, ∞], we obtain sufficient conditions for theuniform stability and uniformly asymptotic stability of the zero solution of theequation, the results in paper [7] are improved.

关键词： infinite delay uniform stability uniformly asymptotic stability