Global attractor for the damped Benjamin–Bona–Mahony equations on R1

We utilize a new necessary and sufficient condition to verity the asymptotic compactness of an evolution equation defined in an unbounded domain, which involves the Littlewood–Paley projection operators. We then use this condition to prove the existence of an attractor for the damped Benjamin–Bona–Mahony equation in the phase space H ¹(R ¹) by showing the solutions are point dissipative and asymptotically compact. Moreover the attractor is in fact smoother and it belongs to H ^3/2?? for every ?>0.     

Global attractors and approximate inertial

An abstract nonautonomous differential equation, u' + Au + F(u) = f ( t ) , is considered using assumptions appropriate for systems of reaction-diffusion equations on multi-dimensional spatial domains. A priori estimates establish the existence of absorbing balls in relevant function spaces, and nonsequently the existence of a global attractor is verified in the associated skew-product flow. It is also shown that approximate inertial manifolds exist for this equation. These are finite-dimensional manifolds which have exponentially attracting neighborhoods under the flow. The dimension of the manifold and the thickness of the attracting neighborhood are inversely related.     

Densities for unbalanced measures of a linear Cantor set

Define a linear Cantor set C to be the attractor of a linear iterated function system fj （x） =rjx ＋ bj（j = 1,2,…,N）, on the line satisfying the sures with respect to C,we study the centered upper and the centered lower density for Ф（t） = t^s withunnatural choices and with natural choices of s.     

The dimension of attractor of the 2D g-Navier-Stokes equations

The g-Navier-Stokes equations in spatial dimension 2 were introduced by Roh as

     

新的切换四涡卷超混沌系统及其电路实现

构建了新的包含2个子系统的切换四涡卷超混沌系统,2个子系统之间既相互关联又相互切换.分析了2个子系统的分岔图、平衡点的稳定性、Lyapunov指数以及动力学行为的演化过程.设计了实现切换四涡卷超混沌系统的电路,系统以时间依赖和状态依赖两种切换律进行任意切换和自主切换,仅用一个电路就能实现2个子系统的切换功能.     

一类推广的BBM方程的强吸引子

主要研究了推广的Benjamin-Bona-Mahony（BBM）方程的解的渐近行为,通过证明半群的渐近紧性证明了方程在H)_per²（Ω）中全局吸引子的存在性.     

一类高阶差分方程非负解的全局行为(英文)

This paper is concerned with the following nonlinear difference equation:x_n+1=sum from i=1 to l A_six_n-si/B+C multiply from j=1 to k x_n-tj +D_xn,n=0,1,…（1.1）.The more simple suffcient conditions of asymptotic stability are obtained by using a smart technique,which extends and includes partially corresponding results obtained in the references [6-9].The global behavior of the solutions is investigated.In addition,in order to support analytic results,some numerical simulations to the special equations are presented.