On Structured Perturbations of Positive Semigroups

TL;DR

This paper extends perturbation theory for positive semigroups on Banach lattices, providing new results applicable to domain perturbations, boundary feedback in heat equations, and derivative perturbations.

Contribution

It generalizes existing perturbation results for positive $C_0$-semigroups and introduces a Weiss--Staffans type perturbation theorem for generators on Banach lattices.

Findings

Extended perturbation results for positive semigroups on AM- and AL-spaces.

Derived a Weiss--Staffans type perturbation theorem for generators.

Applied results to heat equation boundary feedback and derivative perturbations.

Abstract

In this note we generalize perturbation results for positive $C_0$-semigroups on AM- and AL-spaces and give a Weiss--Staffans type perturbation result for generators of positive semigroups on Banach lattices. The abstract results are applied to domain perturbations of generators, a heat equation with boundary feedback and perturbations of the first derivative.