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UNIFORM ATTRACTOR FOR NONAUTONOMOUS INCOMPRESSIBLE NON-NEWTONIAN FLUID WITH A NEW CLASS OF EXTERNAL FORCES 被引量:6
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作者 赵才地 贾晓琳 杨新波 《Acta Mathematica Scientia》 SCIE CSCD 2011年第5期1803-1812,共10页
This paper is joint with [27]. The authors prove in this article the existence and reveal its structure of uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonian fluid with a new class of e... This paper is joint with [27]. The authors prove in this article the existence and reveal its structure of uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonian fluid with a new class of external forces. 展开更多
关键词 uniform attractor incompressible non-Newtonian fluid new class of external forces
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Uniform attractors for non-autonomous Klein-Gordon-Schrdinger lattice systems 被引量:3
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作者 黄锦舞 韩晓莹 周盛凡 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第12期1597-1607,共11页
The existence of a compact uniform attractor for a family of processes corre- sponding to the dissipative non-autonomous Klein-Gordon-SchrSdinger lattice dynamical system is proved. An upper bound of the Kolmogorov en... The existence of a compact uniform attractor for a family of processes corre- sponding to the dissipative non-autonomous Klein-Gordon-SchrSdinger lattice dynamical system is proved. An upper bound of the Kolmogorov entropy of the compact uniform attractor is obtained, and an upper semicontinuity of the compact uniform attractor is established. 展开更多
关键词 compact uniform attractor NON-AUTONOMOUS Klein-Gordon-SchrSoinger lattice system Kolmogorov entropy upper semicontinuity
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Global Existence, Asymptotic Behavior and Uniform Attractors for Damped Timoshenko Systems
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作者 HU Wen-song QIN Yu-ming 《Chinese Quarterly Journal of Mathematics》 2017年第3期305-321,共17页
In this paper, we consider the Timoshenko system as an initial-boundary value problem in a one-dimensional bounded domain. And then we establish the global existence and asymptotic behavior of solution by using the se... In this paper, we consider the Timoshenko system as an initial-boundary value problem in a one-dimensional bounded domain. And then we establish the global existence and asymptotic behavior of solution by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor by using the method of uniform contractive function. The main advantage of this method is that we need only to verify compactness condition with the same type of energy estimate as that for establishing absorbing sets. 展开更多
关键词 Timoshenko systems global existence semigroup methods asymptotic behavior uniform attractors
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Global Existence,Asymptotic Behavior and Uniform Attractors for a Third Order in Time Dynamics
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作者 曹洁 《Chinese Quarterly Journal of Mathematics》 2016年第3期221-236,共16页
In this paper, a third order(in time) partial differential equation in R^n is con-sidered. By using semigroup method and constructing Lyapunov function, we establish the global existence, asymptotic behavior and uni... In this paper, a third order(in time) partial differential equation in R^n is con-sidered. By using semigroup method and constructing Lyapunov function, we establish the global existence, asymptotic behavior and uniform attractors in nonhomogeneous case. In addition, we also obtain the results of well-uosedness in semilinear case. 展开更多
关键词 third order in time dynamics WELL-POSEDNESS asymptotic behavior uniform attractors
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Global Existence, Asympotic Behavior and Uniform Attractors for Thermoelastic Systems
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作者 LI Jiao-long QIN Yu-ming 《Chinese Quarterly Journal of Mathematics》 2017年第3期221-237,共17页
In this paper, we first establish the global existence and asymptotic behavior of solutions by multiplicative techniques, then further prove the existence of a uniform attractor for a thermoelastic system by using the... In this paper, we first establish the global existence and asymptotic behavior of solutions by multiplicative techniques, then further prove the existence of a uniform attractor for a thermoelastic system by using the method of uniform contractive functions. We finally investigate an alternative result of solutions for the semilinear thermoelastic systems by virtue of the semigroup method. 展开更多
关键词 thermoelastic systems global existence asymptotic behavior uniform attractors semigroup methods
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Global Existence,Asymptotic Behavior and Uniform Attractors of Timoshenko Systems with Gurtin-Pipkin Thermal Law
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作者 郑秀珍 《Chinese Quarterly Journal of Mathematics》 2016年第3期307-330,共24页
In this paper,we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques,then further prove the existence of a uniform attractor for Timosh... In this paper,we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques,then further prove the existence of a uniform attractor for Timoshenko systems with Gurtin-Pipkin thermal law by using the method of uniform contractive functions.The main advantages of this method is that we need only to verify compactness condition with the same type of energy estimates as that for establishing absorbing sets.Moreover,we also investigate an alternative result of solutions to the semilinear Timoshenko systems by virtue of the semigroup method. 展开更多
关键词 Timoshenko systems global existence asymptotic behavior uniform attractors semigroup methods
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Dimension of the Uniform Attractor for a Non-autonomous Semilinear Thermoelastic Problem
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作者 李红艳 周盛凡 《Northeastern Mathematical Journal》 CSCD 2008年第4期337-353,共17页
In this paper, we prove the existence of a uniform attractor for the process associated with a non-antonomous semilinear thermoelastic problem. And under the certain parameter, we obtain an upper bound for the Hausdor... In this paper, we prove the existence of a uniform attractor for the process associated with a non-antonomous semilinear thermoelastic problem. And under the certain parameter, we obtain an upper bound for the Hausdorff dimension of the uniform attractor. 展开更多
关键词 uniform attractor thermoelastic problem Hansdorff dimension
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Uniform Attractors for a Non-Autonomous Thermoviscoelastic Equation with Strong Damping
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作者 Zhiyong Ma 《Journal of Applied Mathematics and Physics》 2018年第12期2475-2497,共23页
This paper considers the existence of uniform attractors for a non-autonomous thermoviscoelastic equation with strong damping in a bounded domain Ω&#8838;Rn(n≥1) by establishing the uniformly asymptotic compactn... This paper considers the existence of uniform attractors for a non-autonomous thermoviscoelastic equation with strong damping in a bounded domain Ω&#8838;Rn(n≥1) by establishing the uniformly asymptotic compactness of the semi-process generated by the global solutions. 展开更多
关键词 Thermoviscoelastic EQUATION uniform attractorS STRONG DAMPING
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Global Existence,Asymptotic Behavior and Uniform Attractors for Non-autonomous Thermoelastic Systems 被引量:2
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作者 Yu-ming QIN Tian-hui WEI Jia REN 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2016年第4期1015-1034,共20页
In this paper, we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor for a no... In this paper, we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor for a non-autonomous thermoelastic system by using the method of uniform contractive functions. The main advantage of this method is that we need only to verify compactness condition with the same type of energy estimates as that for establishing absorbing sets. Moreover, we also investigate an alternative result of solutions to the semilinear thermoelastic systems by virtue of the semigroup method. 展开更多
关键词 Thermoelastic systems global existence asymptotic behavior uniform attractors semigroupmethods
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Uniform Attractors for Non-autonomous Brinkman-Forchheimer Equations with Delay 被引量:2
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作者 Jum-Ran KANG Jong-Yeoul PARK 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第5期993-1006,共14页
In this paper, we prove the existence of a uniform attractor for non-autonomous Brinkman-Forchheimer equations with general delay and time-dependent external force.
关键词 Brinkman-Forchheimer equations uniform attractor DELAY translation compact
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Existence of the Uniform Attractors for the Nonautonomous Suspension Bridge Equations with Strong Damping 被引量:1
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作者 Qiao Zhen MA 《Journal of Mathematical Research and Exposition》 CSCD 2010年第2期277-285,共9页
In this paper we show the existence of the uniform attractors for the family of processes corresponding to the suspension bridge equations in H02 × L2 by a new concept of Condition (C*) and the enegy estimats ... In this paper we show the existence of the uniform attractors for the family of processes corresponding to the suspension bridge equations in H02 × L2 by a new concept of Condition (C*) and the enegy estimats methods. 展开更多
关键词 suspension bridge equations uniform attractors Condition (C*) uniform condition(C).
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EXISTENCE OF THE UNIFORM TRAJECTORY ATTRACTOR FOR A 3D INCOMPRESSIBLE NON-NEWTONIAN FLUID FLOW 被引量:2
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作者 汪承志 张明书 赵才地 《Acta Mathematica Scientia》 SCIE CSCD 2018年第1期187-202,共16页
This paper studies the trajectory asymptotic behavior of a non-autonomous in- compressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajector... This paper studies the trajectory asymptotic behavior of a non-autonomous in- compressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajectory attractor for the translation semigroup acting on the united trajectory space. 展开更多
关键词 incompressible non-Newtonian fluid uniform trajectory attractor topological space
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Uniform Exponential Attractors for Non-Autonomous Strongly Damped Wave Equations 被引量:1
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作者 Hongyan Li 《Journal of Applied Mathematics and Physics》 2014年第8期783-794,共12页
In this paper, we study the existence of exponential attractors for strongly damped wave equations with a time-dependent driving force. To this end, the uniform H?lder continuity is established to the variation of the... In this paper, we study the existence of exponential attractors for strongly damped wave equations with a time-dependent driving force. To this end, the uniform H?lder continuity is established to the variation of the process in the phase apace. In a certain parameter region, the exponential attractor is a uniformly exponentially attracting time-dependent set in the phase apace, and is finite-dimensional no matter how complex the dependence of the external forces on time is. On this basis, we also obtain the existence of the infinite-dimensional uniform exponential attractor for the system. 展开更多
关键词 EXPONENTIAL attractor uniform attractor STRONGLY DAMPED Wave Equation
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带有分布时滞吊桥方程一致吸引子
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作者 王素萍 岳晓红 邵旭馗 《安徽大学学报(自然科学版)》 CAS 北大核心 2024年第4期1-9,共9页
考虑当依赖于时间的外力项平移有界而非平移紧时,内部反馈阻尼项含有分布时滞的以矩形板为模型的吊桥方程解的长时间动力学行为.首先,应用单调极大算子理论讨论了该方程解的适定性,进一步应用压缩函数方法证明过程族是一致渐近紧的,从... 考虑当依赖于时间的外力项平移有界而非平移紧时,内部反馈阻尼项含有分布时滞的以矩形板为模型的吊桥方程解的长时间动力学行为.首先,应用单调极大算子理论讨论了该方程解的适定性,进一步应用压缩函数方法证明过程族是一致渐近紧的,从而得到一致吸引子的存在性. 展开更多
关键词 吊桥方程 分布时滞 单调极大算子 一致吸引子
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ATTRACTORS OF NONAUTONOMOUS SCHR?DINGER EQUATIONS
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作者 刘玉荣 刘曾荣 郑永爱 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第2期180-189,共10页
The long-time behaviour of a two-dimensional nonautonomous nonlinear Schrodinger equation is considered. The existence! of uniform attractor is proved and the upper bound of the uniform attractor's Housdorff dimen... The long-time behaviour of a two-dimensional nonautonomous nonlinear Schrodinger equation is considered. The existence! of uniform attractor is proved and the upper bound of the uniform attractor's Housdorff dimension is given. 展开更多
关键词 nonautonomous Schrodinger equations uniform attractor Hausdorff dimension
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Attractors of Dissipative Soliton Equation
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作者 田立新 徐振源 刘曾荣 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第6期571-578,共8页
In the paper ,we study longtime dynamic behavior of dissipative soliton equation existence of attractor ,geometrical structure of attractor dynamic behavior under the parametric perturbation of dissipative soliton equ... In the paper ,we study longtime dynamic behavior of dissipative soliton equation existence of attractor ,geometrical structure of attractor dynamic behavior under the parametric perturbation of dissipative soliton equation.estimate of fractal dimension of attractor. 展开更多
关键词 attractor. uniform absoroing set. fractal dimension. dissipativesolition equation. squeezing proerty and invanant cone proper-ty
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一类时滞抛物方程一致随机吸引子的存在性 被引量:1
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作者 龚婷 黎亚雨 陈桂玲 《吉林大学学报(理学版)》 CAS 北大核心 2023年第2期203-213,共11页
考虑一类带加性噪声和非自治外力项的时滞抛物方程在光滑有界域上一致随机吸引子的存在性.首先通过对解的一致估计,得到方程的解具有关于符号空间的闭的一致拉回吸收集;然后由Sobolev嵌入定理和Arzela-Ascoli定理得到解的一致拉回紧性;... 考虑一类带加性噪声和非自治外力项的时滞抛物方程在光滑有界域上一致随机吸引子的存在性.首先通过对解的一致估计,得到方程的解具有关于符号空间的闭的一致拉回吸收集;然后由Sobolev嵌入定理和Arzela-Ascoli定理得到解的一致拉回紧性;最后证明一致随机吸引子的存在唯一性. 展开更多
关键词 一致随机吸引子 时滞 白噪声 存在性
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带线性记忆和结构阻尼的非自治Kirchhoff型板方程的一致吸引子
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作者 徐玲 白雪 张娟娟 《应用数学》 北大核心 2023年第4期831-844,共14页
本文试图研究带线性记忆和结构阻尼的非自治Kirchhoff型板方程的一致吸引子的存在性.为此,引入一个新的变量η,将先验估计与收缩函数的方法相结合,证明一致有界吸收集和一致渐近紧性,最终得到一致吸引子的存在性.
关键词 板方程 线性记忆 结构阻尼 Kirchhoff型 一致吸引子
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Z^(N)上非自治Schrödinger格点系统的随机一致指数吸引子
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作者 林柔 赵敏 张金璐 《温州大学学报(自然科学版)》 2023年第4期1-12,共12页
主要研究Z^(N)上具有可乘白噪声和拟周期外力的非自治随机Schrödinger格点系统的随机一致指数吸引子的存在性.首先,通过Ornstein-Uhlenbeck过程将带白噪声的系统转化为random系统;然后,证明联合连续非自治随机动力系统的随机指数... 主要研究Z^(N)上具有可乘白噪声和拟周期外力的非自治随机Schrödinger格点系统的随机一致指数吸引子的存在性.首先,通过Ornstein-Uhlenbeck过程将带白噪声的系统转化为random系统;然后,证明联合连续非自治随机动力系统的随机指数吸引子的存在性;最后,将得到的随机指数吸引子投影到相空间证得随机一致指数吸引子的存在性. 展开更多
关键词 Schrödinger格点系统 随机一致指数吸引子 Z^(N)格 拟周期外力 可乘白噪声
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非自治Cahn-Hilliard方程的一致吸引子 被引量:6
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作者 董超雨 姜金平 张晓明 《郑州大学学报(理学版)》 CAS 北大核心 2014年第2期21-23,30,共4页
研究了非自治Cahn-Hilliard方程的长时间动力学行为,证明了该方程一致吸引子的存在性.利用含有两个参数的过程族来描述无穷维动力系统的方法,并借助Young不等式、Sololev嵌入定理、插值不等式及Gronwall不等式等技巧,证明了Cahn-Hilliar... 研究了非自治Cahn-Hilliard方程的长时间动力学行为,证明了该方程一致吸引子的存在性.利用含有两个参数的过程族来描述无穷维动力系统的方法,并借助Young不等式、Sololev嵌入定理、插值不等式及Gronwall不等式等技巧,证明了Cahn-Hilliard方程在空间L2(Ω)中存在一致吸引子. 展开更多
关键词 非自治 CAHN-HILLIARD方程 一致吸引子
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