Weak stabilization of a transmission Euler-Bernoulli plate equation with force and moment feedback

TL;DR

This paper investigates the energy decay of a transmission Euler-Bernoulli plate equation with force and moment feedback, demonstrating at least logarithmic decay using Carleman estimates and resolvent analysis.

Contribution

It introduces a novel application of Carleman estimates to establish logarithmic energy decay for the transmission plate equation with feedback.

Findings

Energy decays at least logarithmically over time.

Uses Carleman estimates to derive resolvent estimates.

Provides a mathematical framework for stabilization analysis.

Abstract

In this paper we will study the asymptotic behaviour of the energy decay of a transmission plate equation with force and moment feedback. Precisly, we shall prove that the energy decay at least logarithmically over the time. The method consist to use the classical second order Carleman estimate to estabish a resolvent estimate which provide by the famous Burq's result [Bur98] the kind of decay above mentionned.