On the controllability of some equations of Sobolev-Galpern type

TL;DR

This paper investigates the controllability of Sobolev-Galpern type equations, demonstrating limitations with fixed support controls and proposing conditions under which moving support controls can achieve controllability.

Contribution

It introduces new controllability results for Sobolev-Galpern equations, highlighting the necessity of moving support controls for effective control.

Findings

Fixed support controls cannot drive the equations to zero.

Moving support controls can achieve controllability under certain conditions.

The paper establishes assumptions on the support movement for control success.

Abstract

In this paper we deal with the controllability problem for some Sobolev type equations. We show that the equations cannot be driven to zero if the control region is strictly supported within the domain. Nevertheless, we also prove that it is possible to control the equations using controls which have a moving support, under some assumptions on its movement.