On the admissibility of observation operators in the context of maximal regularity

TL;DR

This paper investigates the stability of admissible observation operators for perturbed evolution equations within the framework of maximal regularity, demonstrating invariance under certain non-autonomous perturbations and illustrating with practical examples.

Contribution

It proves the invariance of maximal regularity and admissibility of observation operators under non-autonomous Miyadera-Voigt perturbations, extending the theoretical understanding of such systems.

Findings

Maximal $L^p$-regularity remains invariant under specific perturbations.

Admissibility of observation operators is preserved under these perturbations.

Practical examples demonstrate the theoretical results in non-autonomous parabolic and boundary condition problems.

Abstract

We study admissible observation operators for perturbed evolution equations using the concept of maximal regularity. We first show the invariance of the maximal $L^p$-regularity under non-autonomous Miyadera-Voigt perturbations. Second, we establish the invariance of admissibility of observation operators under such a class of perturbations. Finally, we illustrate our result with two examples, one on a non-autonomous parabolic system, and the other on an evolution equation with mixed boundary conditions and a non-local perturbation.