On Perturbations of Generators of $C_0$-Semigroups

TL;DR

This paper introduces a new operator-theoretic perturbation result for generators of $C_0$-semigroups, extending classical theorems and applicable to boundary condition perturbations.

Contribution

It provides a novel perturbation theorem for $C_0$-semigroup generators, generalizing existing results like Weiss-Staffans and Miyadera-Voigt theorems.

Findings

Extended perturbation results to unbounded boundary perturbations

Unified framework for classical perturbation theorems

Illustrated applications to boundary condition modifications

Abstract

We present a perturbation result for generators of $C_0$-semigroups which can be considered as an operator theoretic version of the Weiss-Staffans perturbation theorem for abstract linear systems. The result are illustrated by applications to the Desch-Schappacher, the Miyadera Voigt perturbation theorems, and to unbounded perturbations of the boundary conditions of a generator.