Non-autonomous Desch-Schappacher perturbations

TL;DR

This paper studies time-dependent Desch-Schappacher perturbations in non-autonomous abstract Cauchy problems and applies the results to elliptic differential operators on L^p-spaces, advancing understanding of their behavior.

Contribution

It introduces a framework for analyzing non-autonomous Desch-Schappacher perturbations and applies it to elliptic operators, extending existing theory to time-dependent cases.

Findings

Established well-posedness for non-autonomous perturbations

Extended analysis to elliptic differential operators on L^p-spaces

Provided new tools for studying time-dependent operator perturbations

Abstract

We consider time-dependent Desch-Schappacher perturbations of non-autonomous abstract Cauchy problems and apply our result to non-autonomous uniformly strongly elliptic differential operators on $\mathrm{L}^p$-spaces.