退化C_0半群的扰动

Perturbations of Degenerate Semigroup

讨论多值线性算子A生成的退化C_0半群在线性算子B下的扰动问题。在退化C_0半群的生成定理的基础上,本文对于B为单值有界,相对A有界,以及B为多值线性算子的情况分别给出了A在B下的扰动A+B生成退化C_0半群的条件。

In this paper we discuss perturbations of degenerate C0 semigroup whose geneator is a multi - valued linear operator A perturbated by another linear operator B. Based on the generation theorem, several different conditions which enable the perturbation A + B to be the generator of degenerate C0 semigroup are given when B is single - valued bounded, relatively bounded with respect to A, and multi - valued operator.