This work is devoted to the following suspension bridge with state-dependent delay: . The main goal of this paper is to investigate the long-time behavior of the system. Under suitable hypothesis, the quasi-stability ...This work is devoted to the following suspension bridge with state-dependent delay: . The main goal of this paper is to investigate the long-time behavior of the system. Under suitable hypothesis, the quasi-stability estimates of the system are established, based on which the existence of global attractor with finite fractal dimension is obtained. Furthermore, the existence of exponential attractor is proved.展开更多
在该文中,令E表示一个迭代函数系统(X,T_1,…,T_m)的吸引子.定义连续自映射f:E→E为f(x)=T_j^(-1)(x),x∈T_j(E),j=1,…,m.给定φ∈C_R(E),令K_φ(δ,n)=sup{sum from k=0 to n-1{φ(f^kx)-φ(f^ky)]|:y∈B_x(δ,n)},这里B_x(δ,n)表示B...在该文中,令E表示一个迭代函数系统(X,T_1,…,T_m)的吸引子.定义连续自映射f:E→E为f(x)=T_j^(-1)(x),x∈T_j(E),j=1,…,m.给定φ∈C_R(E),令K_φ(δ,n)=sup{sum from k=0 to n-1{φ(f^kx)-φ(f^ky)]|:y∈B_x(δ,n)},这里B_x(δ,n)表示Bowen球.取一个扩张常数ε,记K_φ=sup_nK_φ(ε,n),定义υ(E)={φ:K_φ<∞).对f:E→E,作为Ruelle的一个定理[3,定理2.1]的一个应用,我们证明每个φ∈υ(E)具有惟一的平衡态.此结果推广了文献[12]中的主要结果.展开更多
文摘This work is devoted to the following suspension bridge with state-dependent delay: . The main goal of this paper is to investigate the long-time behavior of the system. Under suitable hypothesis, the quasi-stability estimates of the system are established, based on which the existence of global attractor with finite fractal dimension is obtained. Furthermore, the existence of exponential attractor is proved.
文摘在该文中,令E表示一个迭代函数系统(X,T_1,…,T_m)的吸引子.定义连续自映射f:E→E为f(x)=T_j^(-1)(x),x∈T_j(E),j=1,…,m.给定φ∈C_R(E),令K_φ(δ,n)=sup{sum from k=0 to n-1{φ(f^kx)-φ(f^ky)]|:y∈B_x(δ,n)},这里B_x(δ,n)表示Bowen球.取一个扩张常数ε,记K_φ=sup_nK_φ(ε,n),定义υ(E)={φ:K_φ<∞).对f:E→E,作为Ruelle的一个定理[3,定理2.1]的一个应用,我们证明每个φ∈υ(E)具有惟一的平衡态.此结果推广了文献[12]中的主要结果.
