Controllability of a viscoelastic plate using one boundary control in displacement or bending

TL;DR

This paper investigates the controllability of a viscoelastic plate and demonstrates that it retains the controllability properties of a purely elastic plate when controlled via boundary displacement or bending.

Contribution

It shows that a viscoelastic plate of Maxwell-Boltzmann type inherits the controllability properties of an elastic plate, using operator and moment methods.

Findings

Viscoelastic plate inherits elastic plate controllability.

Controllability is achieved via boundary displacement or bending.

Operator and moment methods are used for proof.

Abstract

In this paper we consider a viscoelastic plate (linear viscoelasticity of the Maxwell-Boltzmann type) and we compare its controllability properties with the (known) controllability of a purely elastic plate (the control acts on the boundary displacement or bending). By combining operator and moment methods, we prove that the viscoelastic plate inherits the controllability properties of the purely elastic plate.