积分半群的表示及其在抽象积微分方程中的应用(英文)

On Representation of Integrated Semigroups and Application to Abstract Integrodifferential Equation

讨论了积分半群与C0半群的关系,给出了用一组C0半群的积分序列的极限表示积分半群的表示公式.利用该公式证明了积分半群的其它表示式.最后用该公式给出了求解一类抽象积微分方程的新方法.

In this paper, we discuss the relations between C0 -semigroups andintegrated semigroups and give a representation formulas of integrated semigroups by the convergence of integral of a sequence C0-semigroups. Using the representation, we prove other fomulas of integrated semigroups. Finally, we also consider abstract integrodifferential equation and present a new method to find solution.