• Multiplicative perturbations of local 𝐶-semigroups

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      https://www.ias.ac.in/article/fulltext/pmsc/125/01/0045-0055

    • Keywords

       

      Local 𝐶-semigroup; generator; abstract Cauchy problem; perturbation.

    • Abstract

       

      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.

    • Author Affiliations

       

      Chung-Cheng Kuo1

      1. Department of Mathematics, Fu Jen University, New Taipei City, Taiwen 24205, Republic of China
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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