Exact Controllability for a Refined Stochastic Plate Equation

TL;DR

This paper proves the exact controllability of a multidimensional refined stochastic plate equation using a new Carleman estimate, highlighting the necessity of specific controls for controllability.

Contribution

It introduces a refined stochastic plate model and establishes its exact controllability with interior and boundary controls, using a novel Carleman estimate.

Findings

Exact controllability achieved with two interior and two boundary controls.

Lack of controllability if fewer controls are used.

New global Carleman estimate developed for the analysis.

Abstract

A widely used stochastic plate equation is the classical plate equation perturbed by a term of It\^o's integral. However, it is known that this equation is not exactly controllable even if the controls are effective everywhere in both the drift and the diffusion terms and also on the boundary. In some sense, this means that some key feature has been ignored in this model. Then, a one-dimensional refined stochastic plate equation is proposed and its exact controllability is established in [28]. In this paper, by means of a new global Carleman estimate, we establish the exact controllability of the multidimensional refined stochastic plate equation with two interior controls and two boundary controls. Moreover, we give a result about the lack of exact controllability, which shows that the action of two interior controls and at least one boundary control is necessary.