Multiplicative perturbations of local 𝐶-semigroups

Proceedings Mathematical Sciences

Chung-Cheng Kuo¹ 

[1] Department of Mathematics, Fu Jen University, New Taipei City, Taiwen 0, Republic of China$$

关键词: Local 𝐶-semigroup;    generator;    abstract Cauchy problem;    perturbation.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper, we establish some left and right multiplicative perturbation theorems concerning local 𝐶-semigroups when the generator 𝐴 of a perturbed local 𝐶-semigroup $S(cdot)$ may not be densely defined and the perturbation operator 𝐵 is a bounded linear operator from $overline{D(A)}$ into 𝑅(𝐶) such that 𝐶𝐵=𝐵𝐶 on $overline{D(A)}$, which can be applied to obtain some additive perturbation theorems for local 𝐶-semigroups in which 𝐵 is a bounded linear operator from $[D(A)]$ into 𝑅(𝐶) such that 𝐶𝐵=𝐵𝐶 on $overline{D(A)}$. We also show that the perturbations of a (local) 𝐶-semigroup $S(cdot)$ are exponentially bounded (resp., norm continuous, locally Lipschitz continuous, or exponentially Lipschitz continuous) if $S(cdot)$ is.

【 授权许可】

Unknown