Feedback stabilization of a simplified model of fluid-structure interaction on a tree

TL;DR

This paper demonstrates that a simplified fluid-structure interaction model on a tree exhibits exponential energy decay under certain conditions, using frequency domain analysis and resolvent techniques.

Contribution

It introduces a novel stability analysis for a simplified fluid-structure interaction model on a tree, establishing exponential decay of energy.

Findings

Energy of solutions decays exponentially over time

Stability proven under specific conditions

Frequency domain and resolvent analysis techniques used

Abstract

In this paper we study the dynamic feedback stability for a simplified model of fluid-structure interaction on a tree. We prove that, under some conditions, the energy of the solutions of the system decay exponentially to zero when the time tends to infinity. Our technique is based on a frequency domain method and a special analysis for the resolvent.