# Stabilization for vibrating plate with singular structural damping

## TL;DR

This paper analyzes the decay behavior of a vibrating Euler-Bernoulli plate with localized singular damping, demonstrating that the system's energy diminishes logarithmically over time using advanced frequency domain and Carleman estimates.

## Contribution

It introduces a novel approach combining frequency domain analysis and Carleman estimates to establish logarithmic energy decay for plates with singular boundary damping.

## Key findings

- Energy decays logarithmically over time
- Established decay estimates using Carleman techniques
- Extended analysis to systems with localized singular damping

## Abstract

We consider the dynamic elasticity equation, modeled by the Euler-Bernoulli plate equation, with a locally distributed singular structural (or viscoelastic ) damping in a boundary domain. Using a frequency domain method combined, based on the Burq's result, combined with an estimate of Carleman type we provide precise decay estimate showing that the energy of the system decays logarithmically as the type goes to the infinity.