Attractors and dimension of dissipative lattice systems
Attractors and dimension of dissipative lattice systems
复制标题
DOI：
10.1016/j.jde.2005.06.024
复制
发表时间：
2006-05
影响因子：
2.4
通讯作者：
Shengfan Zhou;W. Shi
中科院分区：
文献类型：
--
作者：
Shengfan Zhou;W. Shi
本文利用[Q.F.妈，S.H. Wang，C.K.钟，半群全局吸引子存在的充要条件及其应用，印第安纳州，数学学报，51（6）（2002），1541-1559.]，我们证明了[S]中给出的条件。Zhou，Attractor and Approximations for lattice dynamics systems，J. Differential Equations 200（2004）342-368。是离散Hilbert空间上一般格系所对应的半群存在全局吸引子的一个充分必要条件。作为应用，我们考虑了包含所有有界序列的离散加权空间中二阶格系统全局吸引子的存在性。最后，我们证明了一阶和部分耗散晶格系统对应的（部分耗散）反应扩散方程和二阶耗散晶格系统对应的强阻尼波方程的整体吸引子具有有限的分形维数，如果非线性项的导数是小的起源。
In this paper, by using the argument in [Q.F. Ma, S.H. Wang, C.K. Zhong, Necessary and sufficient conditions for the existence of global attractor for semigroup and application, Indiana Univ. Math. J., 51(6) (2002), 1541–1559.], we prove that the condition given in [S. Zhou, Attractors and approximations for lattice dynamical systems, J. Differential Equations 200 (2004) 342–368.] for the existence of a global attractor for the semigroup associated with general lattice systems on a discrete Hilbert space is a sufficient and necessary condition. As an application, we consider the existence of a global attractor for a second-order lattice system in a discrete weighted space containing all bounded sequences. Finally, we show that the global attractor for first-order and partly dissipative lattice systems corresponding to (partly dissipative) reaction–diffusion equations and second-order dissipative lattice systems corresponding to the strongly damped wave equations have finite fractal dimension if the derivative of the nonlinear term is small at the origin.