Approximate and null controllability of a parabolic system with coupling terms of order one

TL;DR

This paper investigates approximate and null controllability for a parabolic system with order-one coupling terms, extending existing results to more general control domains beyond intervals.

Contribution

It provides new controllability conditions for parabolic systems with order-one coupling terms and arbitrary control domains, broadening previous theoretical frameworks.

Findings

Established controllability conditions for systems with non-interval control domains.

Extended existing results from order-zero to order-one coupling terms.

Provided theoretical criteria applicable to more general control configurations.

Abstract

We study two notions of controllability on a parabolic system with coupling terms of order one. Based on existing results on, on one side parabolic systems with coupling terms of order zero, and on the other one parabolic systems with coupling terms of order one where the control domain is an interval, we give here some controllability conditions in the case where the coupling term is of order one and the control domain is not necessarily an interval.