Internal exact controllability for nagdhi shell

TL;DR

This paper investigates the exponential stability and exact controllability of Naghdi shell models with internal dissipation, employing Riemannian geometry and semigroup theory to establish energy decay and control results.

Contribution

It introduces a novel approach combining Riemannian geometry and semigroup theory to prove exponential stability and exact controllability for Naghdi shell models.

Findings

Proved well-posedness of the Naghdi shell model.

Established observability inequalities leading to energy decay.

Demonstrated exact controllability using Russell's principle.

Abstract

In this work we study the exponential stability of the energy associated with a Naghdi shell model with localized internal dissipation. Using several tools from Riemannian Geometry we show the well possedness of the model, via semigroup theory, and obtain observability inequalities which allows to prove the exponential decay of the total energy. As a consequence then we use Russell Principle for obtain exact controllability.