双连续n次积分C半群与一类抽象Cauchy问题的强解

Bi-continuous n-times integrated C-semigroups and the strong solution of Abstract Cauchy problem

为了解决偏微分方程初值问题和一些实际问题,数学家提出了算子半群理论。随着问题的深入,半群理论也不断的发展。F.kühnemund在Banach空间上赋予一个比范数拓扑粗的局部凸拓扑,从而提出双连续半群。结合双连续半群和n次积分半群常胜伟提出了双连续n次积分C半群,并讨论了双连续n次积分C半群的一些相关概念及性质。笔者主要讨论Banach空间上双连续n次积分C半群在抽象Cauchy问题中的应用。利用双连续n次积分C半群的概念和性质,讨论一类抽象Cauchy问题当系数是双连续n次积分C半群的生成元时强解的存在性问题。

In order to solve the initial value problem of partial differential equation and some practical problems,mathematicians propose operator semigroup theory.With the deep study,semigroup theory has been developed.F.kummenemund has given coarser locally convex topology in Banach space than the norm topology,and then,he put forward the Bi-continuous semigroup.Combining with bi-continuous semigroups and n-times integrated semigroups,CHANG Shengwei proposed bi-continuous n-times integrated C semigroups,and discussed some related concepts and properties of bi-continuous n-times integrated C semigroups.In this paper,the application of the bi-continuous n-times integrated C semigroups and Abstract Cauchy problem in Banach space is studied.Using the concepts and properties of the bi-continuous n-times integrated C semigroups,the existence of strong solution of a class of Abstract Cauchy problems is discussed when the coefficient is generator of the bi-continuous n-times integrated C semigroups.