加权空间一阶耗散格点动力系统的吸引子

Attractor of First Order Dissipative Lattice System in Weighted Spaces

运用加权空间的思想研究一阶耗散格点系统。首先,引入指数衰减的权函数,并构造加权空间。接着,在加权空间中对一阶耗散格点系统的解进行先验估计,并给出一阶耗散格点系统有界吸收集的存在性。最后,利用权函数在无穷远处衰减和截尾估计法得到相应半群的渐近紧性,并证明了一阶耗散格点系统全局吸引子的存在性。

By the weighted space the first order dissipative lattice system was studied.Firstly,this paper introduced the weighted function with exponential decay,and gave the corresponding weighted space. Secondly,a priori estimate on the solutions of first order lattice dynamical systems was derived,and then the existence of a bounded absorbing set was proven.Thirdly,by the exponential decay of the weighted function at infinity and the method of end tail estimate,the asymptotic compact of the semigroup and the existence of the global attractor for the first order dissipative lattice system were obtained.