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Squeezing properties of a trapped ion in the running-wave laser beyond the Lamb-Dicke limit 被引量:1
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作者 潘长宁 方卯发 +1 位作者 郑小娟 胡要花 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第6期1549-1553,共5页
Beyond the Lamb-Dicke limit, this paper investigates the squeezing properties of the trapped ion in the travelling- wave laser. It shows that the squeezing properties of the trapped ion in the travelling-wave laser ar... Beyond the Lamb-Dicke limit, this paper investigates the squeezing properties of the trapped ion in the travelling- wave laser. It shows that the squeezing properties of the trapped ion in the travelling-wave laser are strongly affected by the sideband number k, the Lamb-Dicke parameter η and the initial average phonon number. 展开更多
关键词 squeezing properties trapped ion travelling-wave laser beyond Lamb-Dicke limit
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EXPONENTIAL ATTRACTOR FOR THE GENERALIZED SYMMETRIC REGULARIZED LONG WAVE EQUATION WITH DAMPING TERM 被引量:1
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作者 尚亚东 郭柏灵 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第3期283-291,共9页
The global fast dynamics for the generalized symmetric regularized long wave equation with damping term is considered. The squeezing property of the nonlinear semi_group associated with this equation and the existence... The global fast dynamics for the generalized symmetric regularized long wave equation with damping term is considered. The squeezing property of the nonlinear semi_group associated with this equation and the existence of exponential attractor are proved. The upper bounds of its fractal dimension are also estimated. 展开更多
关键词 symmetric regularized long wave equation asymptotic behavior squeezing property exponential attractor
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The Family of Exponential Attractors and Inertial Manifolds for a Generalized Nonlinear Kirchhoff Equations 被引量:3
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作者 Guoguang Lin Xiaomei Liu 《Journal of Applied Mathematics and Physics》 2022年第1期172-189,共18页
In this paper, we study the long-time behavior of a class of generalized nonlinear Kichhoff equation under the condition of n dimension. Firstly, the Lipschitz property and squeezing property of the nonlinear semigrou... In this paper, we study the long-time behavior of a class of generalized nonlinear Kichhoff equation under the condition of n dimension. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup related to the initial-boundary value problem are proved, and then the existence of its exponential attractor is obtained. By extending the space <em>E</em><sub>0</sub> to <em>E<sub>k</sub></em>, a family of the exponential attractors of the initial-boundary value problem is obtained. In the second part, we consider the long-time behavior for a system of generalized Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of a family of the inertial manifolds while such equations satisfy the spectrum interval condition. 展开更多
关键词 A Family of the Exponential Attractors Inertial Fractal Set squeezing Property Spectral Gap Condition A Family of the Inertial Manifolds
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A Family of Exponential Attractors and Inertial Manifolds for a Class of Higher Order Kirchhoff Equations 被引量:1
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作者 Guoguang Lin Yingguo Wang 《Journal of Applied Mathematics and Physics》 2022年第3期900-914,共15页
In this paper, the global dynamics of a class of higher order nonlinear Kirchhoff equations under n-dimensional conditions is studied. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup ... In this paper, the global dynamics of a class of higher order nonlinear Kirchhoff equations under n-dimensional conditions is studied. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup associated with the initial boundary value problem are proved, and the existence of a family of exponential attractors is obtained. Then, by constructing the corresponding graph norm, the condition of a spectral interval is established when N is sufficiently large. Finally, the existence of the family of inertial manifolds is obtained. 展开更多
关键词 Kirchhoff Equation Lipschitz Property squeezing Property a Family of the Exponential Attractors a Family of Inertial Manifolds
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EXPONENTIAL ATTRACTORS FOR A GENERALIZED GINZBURG-LANDAU EQUATION
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作者 高洪俊 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1995年第9期877-882,共6页
Based on the paper [1]. we obtain the existence of exponential attractors for a generalized Ginzburg-Landau equation in one dimension
关键词 generalized Ginzburg-Landau equation. squeezing property.exponential attractor
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The Family of Exponential Attractors and Random Attractors for a Class of Kirchhoff Equations
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作者 Guoguang Lin Chunmeng Zhou 《Journal of Applied Mathematics and Physics》 2021年第12期3143-3154,共12页
To prove the existence of the family of exponential attractors, we first define a family of compact, invariant absorbing sets <em>B<sub>k</sub></em>. Then we prove that the solution semigroup h... To prove the existence of the family of exponential attractors, we first define a family of compact, invariant absorbing sets <em>B<sub>k</sub></em>. Then we prove that the solution semigroup has Lipschitz property and discrete squeezing property. Finally, we obtain a family of exponential attractors and its estimation of dimension by combining them with previous theories. Next, we obtain Kirchhoff-type random equation by adding product white noise to the right-hand side of the equation. To study the existence of random attractors, firstly we transform the equation by using Ornstein-Uhlenbeck process. Then we obtain a family of bounded random absorbing sets via estimating the solution of the random differential equation. Finally, we prove the asymptotic compactness of semigroup of the stochastic dynamic system;thereby we obtain a family of random attractors. 展开更多
关键词 Family of Exponential Attractors Lipschitz Continuous squeezing Property Stochastic Dynamic System Family Random Attractors
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Uniform Exponential Attractors for Second Order Non-autonomous Lattice Dynamical Systems 被引量:1
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作者 Xiao-peng ZHOU Fu-qi YIN Sheng-fan ZHOU 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2017年第3期587-606,共20页
In this paper, the existence of a uniform exponential attractor for a second order non-autonomous lattice dynamical system with quasiperiodic symbols acting on a closed bounded set is considered. Firstly, the existenc... In this paper, the existence of a uniform exponential attractor for a second order non-autonomous lattice dynamical system with quasiperiodic symbols acting on a closed bounded set is considered. Firstly, the existence and uniqueness of solutions for the considered systems which generate a family of continuous processes is shown, and the existence of a uniform bounded absorbing sets for the processes is proved. Secondly, a semigroup defined on a extended space is introduced, and the Lipschitz continuity, a-contraction and squeezing property of this semigroup are proved. Finally, the existence of a uniform exponential attractor for the family of processes associated with the studied lattice dynamical systems is obtained. 展开更多
关键词 uniform exponential attractor quasiperiodic symbols a family of processes squeezing property lattice dynamical systems
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EXPONENTIAL ATTRACTORS OF THE GINZBURG-LANDAU-BBM EQUATIONS IN AN UNBOUNDED DOMAIN 被引量:1
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作者 戴正德 蒋慕蓉 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2001年第4期484-493,共10页
In this paper, the existence of the exponential attractors for the Ginzburg-Landau-BBM equations in an unbounded domain is proved by using weighted function and squeezing property.
关键词 Exponential attractor Ginzburg-Landau-BBM equations unbounded domain weighted function squeezing property
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