摘要
1 引言 众所周知,算子半群数十年的持续发展,已使其形成一个对数学与工程技术问题有重要应用的广泛的数学分支。但迄止今日,围绕这一理论所开展的主要工作仍集中在强连续算子半群(即C_0半群)上。另一方面,算子半群与抽象Cuchy问题有密切的关系。即算子半群是抽象Cauchy问题研究中最有力的工具,而抽象Cauchy问题则是算子半群最显著的应用题材,因此两者是相互促进、共同成长的。
The concept of integrated semigroups was introduced by W. Arendt in 1987. Since then this theory has been developed rapidly,and applied successfully to abstract Cauchy problems. In this paper a survey of this field is given. It consists of ten parts. 1 Introduction; 2 Definitions and properties; 3 Some examples; 4 Generation theorems; 5 Perturbations and approximations; 6 Connections with C-semigroups; 7 Some other problems; 8 First order abstract Cauchy problems; 9 Higer order abstract Cauchy problems; 10 Concluding remarks (some open problems are posed) .
出处
《数学进展》
CSCD
北大核心
1992年第3期257-273,共17页
Advances in Mathematics（China）
基金
国家自然科学基金
