Attractors for locally damped Bresse systems and a unique continuation property

TL;DR

This paper proves the existence of global attractors for locally damped Bresse systems, a model for circular beams, by establishing a unique continuation property using Carleman estimates within a Riemannian geometry framework.

Contribution

It introduces a novel approach to prove attractor existence for Bresse systems with localized damping by developing a unique continuation property using Carleman estimates.

Findings

Existence of global attractors for Bresse systems with localized damping

Development of a unique continuation property for Bresse systems

Application of Riemannian geometry and Carleman estimates in PDE analysis

Abstract

This paper is devoted to Bresse systems, a robust model for circular beams, given by a set of three coupled wave equations. The main objective is to establish the existence of global attractors for dynamics of semilinear problems with localized damping. In order to deal with localized damping a unique continuation property (UCP) is needed. Therefore we also provide a suitable UCP for Bresse systems. Our strategy is to set the problem in a Riemannian geometry framework and see the system as a single equation with different Riemann metrics. Then we perform Carleman-type estimates to get our result.