n次积分C半群与非齐次抽象柯西问题的强解

n-times Integrated C-semigroups and Non-homogeneous Abstract Cauchy Problem

引入了主算子为n次积分C半群生成元的线性非齐次抽象柯西问题强解的概念,讨论了相应抽象柯西问题存在强解的一些充分必要条件及强解的表示式.并给出了一个例子验证结果.

In this paper, we obtain several properties of n-times integrated C-semigroups and their proofs. We also investigate the relations of n-times integrated C-semigroups and the strong solution of corresponding non-homogeneous abstract Cauchy problem, and the representation of strong solution.