Theorical and Numerical Analysis of the Rapid Pointwise Stabilization of Coupled String-Beam Systems

TL;DR

This paper investigates the stabilization and controllability of coupled wave and plate systems, demonstrating high decay rates and providing numerical methods to design feedback laws for exponential stabilization.

Contribution

It offers a theoretical proof of high-rate stabilization and controllability for coupled string-beam systems, along with a numerical approach to construct effective feedback laws.

Findings

Systems can be stabilized with arbitrarily high decay rates

Exact controllability is achievable under general conditions

Numerical methods effectively construct feedback laws for exponential decay

Abstract

We consider a pointwise stabilization problem for a coupled wave and plate equations. We prove under rather general assumptions, that such systems can stabilized so as to have arbitrarily high decay rates and are exactly controllable. We propose a numerical approximation of the model and we study numerically the construction of the feedbak law leading to exponential decay with arbtrarily large rate.