（E_0，E）型渐近光滑映射和耗散波方程

(E_0, E)Asymptotically Smooth Maps And Dissipative Wave Equations

本文在无穷维空间引入（Ｅ_０，Ｅ）型渐近光滑映射的概念，研究了其基本性质和变为Ｅ中渐近光滑映射的条件，我们证明了（Ｅ_０，Ｅ）型吸引子存在性定理和（Ｅ_０，Ｅ）型吸引子转化为Ｅ中吸引子的条件定理，所有结果都应用于一类耗散波方程渐近性态的研究。映射，吸引子。

In this paper, we will introduce the concept of (E0,E) asytmptotilly smooth map in infinite dimehonal space, and study its basic properties and conditions under which it becomes an asymptotically smooth map in E. We prove the existence theorem of (E0,E) attractor and theorems about conditions under which an (E0,E) attractor becomes an attractor in E. All results are appliable to the study of the asymptotic properties of a class of dissipative wave equations.